Researcher Profile and Settings

Affiliation

• Faculty of Engineering　Applied Physics　Quantum Matter Physics

Job Title

• Professor

URL

http://subutu-ap.eng.hokudai.ac.jp/

J-Global ID

• 200901015027018861

Research Interests

• 計算機物理学   金属絶縁体転移   低次元電子系   複雑ネットワーク   臨界系   ランダム   フラクタル   Numerical Physics   Metal-Insulator Transition   Low-dimensional Electron Systems   complex networks   critical systems   random   fractal   

Research Areas

• Natural sciences / Semiconductors, optical and atomic physics

Educational Organization

•  Bachelor's degree program　School of Engineering
•  Master's degree program　Graduate School of Engineering
•  Doctoral (PhD) degree program　Graduate School of Engineering

Education

•        - 1987  Hokkaido University
•        - 1987  Hokkaido University  Graduate School, Division of Engineering

Association Memberships

• American Physical Society   日本物理学会   THE JAPAN SOCIETY OF APPLIED PHYSICS   The Physical Society of JapanThe Japan Society of Applied PhysicsAmerican Physical Society   

Research Activities

Published Papers

• A general model of hierarchical fractal scale-free networks

  Kousuke Yakubo, Yuka Fujiki

  PLOS ONE 17 (3) e0264589 - e0264589 2022/03/21 [Refereed][Not invited]
   

  We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change the network structure. In this model, an FSFN is iteratively formed by replacing each edge in the previous generation network with a small graph called a generator. The choice of generators enables us to control the scale-free property, fractality, and other structural properties of hierarchical FSFNs. We calculate theoretically various characteristic quantities of networks, such as the exponent of the power-law degree distribution, fractal dimension, average clustering coefficient, global clustering coefficient, and joint probability describing the nearest-neighbor degree correlation. As an example of analyses of phenomena occurring on FSFNs, we also present the critical point and critical exponents of the bond-percolation transition on infinite FSFNs, which is related to the robustness of networks against edge removal. By comparing the percolation critical points of FSFNs whose structural properties are the same as each other except for the clustering nature, we clarify the effect of the clustering on the robustness of FSFNs. As demonstrated by this example, the present model makes it possible to elucidate how a specific structural property influences a phenomenon occurring on FSFNs by varying systematically the structures of FSFNs. Finally, we extend our model for deterministic FSFNs to a model of non-deterministic ones by introducing asymmetric generators and reexamine all characteristic quantities and the percolation problem for such non-deterministic FSFNs.
• Identification of intrinsic long-range degree correlations in complex networks

  Yuka Fujiki, Kousuke Yakubo

  Physical Review E 101 (3) 032308  2470-0045 2020/03/18 [Refereed]
  
• General formulation of long-range degree correlations in complex networks

  Yuka Fujiki, Taro Takaguchi, Kousuke Yakubo

  Physical Review E 97 (6) 62308  2470-0053 2018/06/11 [Refereed][Not invited]
   

  We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One joint and four conditional probability distributions are introduced to fully describe long-range degree correlations with respect to degrees k and k′ of two nodes and shortest path length l between them. We present general relations among these probability distributions and clarify the relevance to nearest-neighbor degree correlations. Unlike nearest-neighbor correlations, some of these probability distributions are meaningful only in finite-size networks. Furthermore, as a baseline to determine the existence of intrinsic long-range degree correlations in a network other than inevitable correlations caused by the finite-size effect, the functional forms of these probability distributions for random networks are analytically evaluated within a mean-field approximation. The utility of our argument is demonstrated by applying it to real-world networks.
• Structural instability of large-scale functional networks

  Shogo Mizutaka, Kousuke Yakubo

  PLOS ONE 12 (7) e0181247  1932-6203 2017/07 [Refereed][Not invited]
   

  We study how large functional networks can grow stably under possible cascading overload failures and evaluated the maximum stable network size above which even a small-scale failure would cause a fatal breakdown of the network. Employing a model of cascading failures induced by temporally fluctuating loads, the maximum stable size nmax has been calculated as a function of the load reduction parameter rthat characterizes how quickly the total load is reduced during the cascade. If we reduce the total load sufficiently fast ( r >= r(c)), the network can grow infinitely. Otherwise, nmax is finite and increases with r. For a fixed r(< r(c)), nmax for a scale-free network is larger than that for an exponential network with the same average degree. We also discuss how one detects and avoids the crisis of a fatal breakdown of the network from the relation between the sizes of the initial network and the largest component after an ordinarily occurring cascading failure.
• Fractality and degree correlations in scale-free networks

  Yuka Fujiki, Shogo Mizutaka, Kousuke Yakubo

  EUROPEAN PHYSICAL JOURNAL B 90 (7) 126  1434-6028 2017/07 [Refereed][Not invited]
   

  Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scalefree network fractal. Here we examine the possibility that disassortativity in complex networks is the origin of fractality. To this end, maximally disassortative (MD) networks are prepared by rewiring edges while keeping the degree sequence of an initial uncorrelated scale-free network. We show that there are many MD networks with different topologies if the degree sequence is the same with that of the (u, v)-flower but most of them are not fractal. These results demonstrate that disassortativity does not cause the fractal property of networks. In addition, we suggest that fractality of scale-free networks requires a long-range repulsive correlation, in the sense of the shortest path distance, in similar degrees.
• 21aBS-6 Long-range degree correlations in the (u,v)-flower

  Fujiki Y., Yakubo K.

  Meeting Abstracts of the Physical Society of Japan 一般社団法人日本物理学会 71 2993 - 2993 2189-079X 2016
• General relations between probabilities characterizing long-range degree correlations

  Fujiki Yuka, Takaguchi Taro, Yakubo Kousuke

  Meeting Abstracts of the Physical Society of Japan 一般社団法人 日本物理学会 71 2976 - 2976 2016 

  複雑ネットワークにおける隣接次数相関に関しては、これまでに精力的な研究が行われてきた。しかしながら、ネットワークの複雑さは隣接ノード次数間の相関だけでは記述することはできない。本研究では、長距離のノード間距離を有するノード対に対する次数相関の統計的性質を特徴付ける各種確率関数を導入し、それらの間の一般的関係を提示する。また、長距離次数相関がないネットワークに対するこれら確率関数の関数形を示す。

• Scale-free networks formed by self-organized critical dynamics

  Yamane Yoshihiro, Mizutaka Shogo, Yakubo Kousuke

  Meeting Abstracts of the Physical Society of Japan 一般社団法人 日本物理学会 71 2978 - 2978 2016 

  我々は以前に、過負荷故障カスケード過程に基づくフラクタル複雑ネットワークの形成モデルを提唱した。しかし、自己組織化臨界性（SOC）を有するこのモデルによって形成されたネットワークは、現実ネットワークがもつスケールフリー性を示さない。本研究では、耐性パラメータの分布と優先選択成長のプロセスを導入することで、スケールフリー・フラクタル・ネットワークが自発的に形成されるようなSOCモデルを構築する。

• Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics

  Akitomo Watanabe, Shogo Mizutaka, Kousuke Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 84 (11) 114003  0031-9015 2015/11 [Refereed][Not invited]
   

  We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. In contrast, networks far from criticality have small-world structures. We also observe the crossover behavior from fractal to small-world structure in the network evolution.
• Robustness of scale-free networks to cascading failures induced by fluctuating loads

  Shogo Mizutaka, Kousuke Yakubo

  Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 92 (1) 1550-2376 2015/07/20 [Refereed][Not invited]
   

  Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method show that scale-free networks are more robust against cascading overload failures than Erdos-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.
• Robustness of scale-free networks to cascading failures induced by fluctuating loads

  Shogo Mizutaka, Kousuke Yakubo

  PHYSICAL REVIEW E 92 (1) 12814  2470-0045 2015/07 [Refereed][Not invited]
   

  Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method show that scale-free networks are more robust against cascading overload failures than Erdos-Renyi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.
• Superlinear and sublinear urban scaling in geographical networks modeling cities

  K. Yakubo, Y. Saijo, D. Korosak

  PHYSICAL REVIEW E 90 (2) 22803  1539-3755 2014/08 [Refereed][Not invited]
   

  Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y(N) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y(N) alpha N-beta with beta > 1, if Y(N) represents a creative productivity and the indicator scales sublinearly (beta < 1) if Y(N) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent beta depends on the strength of the geographical constraint in the network formation.
• Catalytic reaction dynamics in inhomogeneous networks

  Akitomo Watanabe, Kousuke Yakubo

  Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 89 (5) 52806  1550-2376 2014/05/12 [Refereed][Not invited]
   

  Biochemical reactions in a cell can be modeled by a catalytic reaction network (CRN). It has been reported that catalytic chain reactions occur intermittently in the CRN with a homogeneous random-graph topology and its avalanche-size distribution obeys a power law with the exponent 4/3 [A. Awazu and K. Kaneko, Phys. Rev. E 80, 010902(R) (2009)PLEEE81539-375510.1103/PhysRevE. 80.010902]. This fact indicates that the catalytic reaction dynamics in homogeneous CRNs exhibits self-organized criticality (SOC). Structures of actual CRNs are, however, known to be highly inhomogeneous. We study the influence of various types of inhomogeneities found in real-world metabolic networks on the universality class of SOC. Our numerical results clarify that SOC keeps its universality class even for networks possessing structural inhomogeneities such as the scale-free property, community structures, and degree correlations. In contrast, if the CRN has inhomogeneous catalytic functionality, the universality class of SOC depends on how widely distributed the number of reaction paths catalyzed by a single chemical species is. © 2014 American Physical Society.
• Catalytic reaction dynamics in inhomogeneous networks

  Akitomo Watanabe, Kousuke Yakubo

  PHYSICAL REVIEW E 89 (5) 2470-0045 2014/05 [Refereed][Not invited]
   

  Biochemical reactions in a cell can be modeled by a catalytic reaction network (CRN). It has been reported that catalytic chain reactions occur intermittently in the CRN with a homogeneous random-graph topology and its avalanche-size distribution obeys a power law with the exponent 4/3 [A. Awazu and K. Kaneko, Phys. Rev. E 80, 010902(R) (2009)]. This fact indicates that the catalytic reaction dynamics in homogeneous CRNs exhibits self-organized criticality (SOC). Structures of actual CRNs are, however, known to be highly inhomogeneous. We study the influence of various types of inhomogeneities found in real-world metabolic networks on the universality class of SOC. Our numerical results clarify that SOC keeps its universality class even for networks possessing structural inhomogeneities such as the scale-free property, community structures, and degree correlations. In contrast, if the CRN has inhomogeneous catalytic functionality, the universality class of SOC depends on how widely distributed the number of reaction paths catalyzed by a single chemical species is.
• Network fragility to overload failures: Influence of the scale-free property

  Shogo Mizutaka, Kousuke Yakubo

  Journal of Complex Networks 2 (4) 413 - 418 2051-1329 2014 [Refereed][Not invited]
   

  Recently, it has been found that scale-free networks are fragile against overload failures. More precisely, the critical node-removal fraction fc or the critical total load Wc at the percolation transition by removing overloaded nodes is an increasing function of the scale-free exponent γ describing the asymptotic degree distribution function as P(k) ∝ k-γ . In the previous work, however, the decrease of the exponent γ reduces the total tolerance for loads. Thus, it is not clear whether scale-free networks are actually fragile against overload failures if the total tolerance dose not change. In this paper, we investigate network robustness against overload failures by calculating analytically the percolation transition point of scale-free networks for various values of γ with keeping the total tolerance constant. Our results show that scale-free networks are surely fragile to overload failures even after excluding the effect of the total tolerance.
• Structural robustness of scale-free networks against overload failures

  Mizutaka Shogo, Yakubo Kousuke

  PHYSICAL REVIEW E 88 (1) 2470-0045 2013/07/08 [Refereed][Not invited]
   

  We study the structural robustness of scale-free networks against overload failures induced by loads exceeding the node capacity, based on analytical and numerical approaches to the percolation problem in which a fixed number of nodes are removed according to the overload probability. Modeling fluctuating loads by random walkers in a network, we find that the degree dependence of the overload probability drastically changes with respect to the total load. We also elucidate that there exist two types of structural robustness of networks against overload failures. One is measured by the critical total load W and the other is by the critical node removal fraction f . Enhancing the scale-free property, networks become fragile in both senses of W and f . By contrast, increasing the node tolerance, scale-free networks become robust in the sense of the critical total load, while they come to be fragile in the sense of the critical node removal fraction. Furthermore, we show that these trends are not affected by degree-degree correlations, although assortative mixing makes networks robust in both senses of W and f . © 2013 American Physical Society. c c c c c c
• Structural robustness of scale-free networks against overload failures.

  Mizutaka S, Yakubo K

  PHYSICAL REVIEW E 88 (1) 12803  1539-3755 2013/07 [Refereed][Not invited]
  
• Overload network failures: An approach from the random-walk model

  Shogo Mizutaka, Kousuke Yakubo

  Proceedings - 2013 International Conference on Signal-Image Technology and Internet-Based Systems, SITIS 2013 630 - 633 2013 [Refereed][Not invited]
   

  We investigate analytically the robustness of scale-free networks against overload failures in percolation and cascading processes. Modeling fluctuating loads in a network by random walkers, it is found that there exist two kinds of robustness of networks against overload failures in the percolation process. One is measured by the critical total load W-rmc and the other is by the critical node removal fraction f-rmc. Enhancing the scale-free property, networks become fragile in both senses. In contrast, the increase of the node tolerance parameter makes scale-free networks robust in the sense of W-rmc but fragile in the sense of f-rmc. In addition, we treat the cascading overload process by considering it as a chain of percolation processes. We show that scale-free networks are robust against cascading overload failures modeled by random walkers, which is opposed to most of the previous results. © 2013 IEEE.
• Testing the Order Parameter of the Anderson Transition

  Kousuke Yakubo, Shogo Mizutaka

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 81 (10) 104707  0031-9015 2012/10 [Refereed][Not invited]
   

  The typical value of the local density of states rho(typ), known as a candidate of the order parameter of the Anderson transition, of two-dimensional disordered electron systems with spin-orbit interactions is studied for assessing the validity of rho(typ) as the order parameter. We show that rho(typ) behaves critically as rho(typ) proportional to (E-c - E)(beta) with beta = 0.466 +/- 0: 095 near the transition point. It is also found that the exponent beta satisfies the scaling relation with the Lipschitz-Holder exponent alpha(0). Furthermore, we demonstrate that fluctuations in rho(typ) at the Anderson transition obey the generalized Gumbel distribution, which is expected to be the universal distribution function of critical fluctuations of order parameters. These results suggest that rho(typ) is a suitable quantity of the order parameter of the Anderson transition.
• Dynamical Crossover in Complex Networks near the Percolation Transition

  Fumiya Kawasaki, Kousuke Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 80 (10) 104001  0031-9015 2011/10 [Refereed][Not invited]
   

  The return probability P-0(t) of random walkers is investigated numerically for several scale-free fractal networks. Our results show that P-0(t) is proportional to t(-ds/2) with the non-integer spectral dimension d(s) as in the case of non-scale free fractal networks. We also study how the diffusion process is affected by the structural crossover from a fractal to a small-world architecture in a network near the percolation transition. It is elucidated that the corresponding dynamical crossover is scaled only by the unique characteristic time t(xi) regardless of whether the network is scale free or not. In addition, the scaling relation d(s) = 2D(f)/d(w) is found to be valid even for scale-free fractal networks, where D-f and d(w) are the fractal and the walk dimensions. These results suggest that qualitative properties of P-0(t) are irrelevant to the scale-free nature of networks.
• Multifractality of complex networks

  Shuhei Furuya, Kousuke Yakubo

  PHYSICAL REVIEW E 84 (3) 36118  1539-3755 2011/09 [Refereed][Not invited]
   

  We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass exponents tau(q) for several deterministic, stochastic, and real-world fractal scale-free networks are nonlinear functions of q, which implies that structural measures of these networks obey the multifractal scaling. In addition, we give a general expression of tau(q) for some class of fractal scale-free networks by a mean-field approximation. The multifractal property of network structures is a consequence of large fluctuations of local node density in scale-free networks.
• Scale-free networks embedded in fractal space

  K. Yakubo, D. Koroak

  Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 83 (6) 1539-3755 2011/06/20 [Refereed][Not invited]
   

  The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to γ=2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture. © 2011 American Physical Society.
• Scale-free networks embedded in fractal space

  K. Yakubo, D. Korosak

  PHYSICAL REVIEW E 83 (6) 66111  2470-0045 2011/06 [Refereed][Not invited]
   

  The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to gamma = 2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture.
• Quantification of Superiority of Broad-Buffer Diodes

  Michio Nemoto, Takashi Yoshimura, Haruo Nakazawa, Kousuke Yakubo

  JAPANESE JOURNAL OF APPLIED PHYSICS 50 (5) 54301  0021-4922 2011/05 [Refereed][Not invited]
   

  We have quantitatively shown the superiority of broad-buffer (BB) diodes over conventional p-i-n diodes, especially with regard to fast and soft reverse recovery, by measuring a new quantity, Gamma, signifying the degree of reverse recovery oscillation (RRO). The performance of switching devices has been evaluated in terms of the forward voltage drop V-F and the reverse recovery loss E-RR up to now, but these quantities cannot assess the inhibition of the RRO, which is another important property of switching devices. The quantity Gamma, defined as the difference between the voltage rating and the RRO threshold power-supply voltage, represents how well the RRO is inhibited. We evaluated the performance of diodes having a variety of doping profiles in the n-drift region by numerically calculating V-F, E-RR, and Gamma and plotting these quantities in a three-dimensional evaluation space. Our device simulation results clearly show that the values of Gamma as well as V-F and E-RR for BB diodes are significantly lower than those for conventional diodes, and that BB diodes should be classified as a new category of diodes in view of their superior reverse recovery characteristics. (C) 2011 The Japan Society of Applied Physics
• Topological transition by dielectric control of exciton wavefunction in thin nanotube structure

  Masami Kumagai, Toshihide Takagahara, Kousuke Yakubo

  SOLID STATE COMMUNICATIONS 151 (9) 663 - 666 0038-1098 2011/05 [Refereed][Not invited]
   

  Dielectric control of the topology of an exciton wavefunction is proposed and investigated theoretically. As we have shown in a previous paper, we can change the topology of an exciton wavefunction in a nanotube structure by controlling the length and radius of the nanotube. This nature yields a new device which utilizes the topology of an exciton wavefunction, however, its control via the structural parameters does not suit it to device applications. We found that the in-situ control can be achieved by changing the ambient dielectric constants of the nanotube structure and we calculated the transition condition of the topology of an exciton wavefunction. (C) 2011 Elsevier Ltd. All rights reserved.
• Asymmetric Propagation of Optical Signals in Graded Plasmonic Chains

  Ming Jie Zheng, Dang Yuan Lei, Kousuke Yakubo, Kin Wah Yu

  PLASMONICS 6 (1) 19 - 27 1557-1955 2011/03 [Refereed][Not invited]
   

  The propagation of optical signals has been studied theoretically and computationally in fully retarded graded plasmonic chains. Asymmetric optical response due to retardation has been observed in various plasmonic chains with gradients in host permittivities, particle sizes, and/or interparticle distances. The range of wavelength-dependent optical response is broadened by the graded effects of host permittivity. Asymmetric propagation ratio is found in the presence of any kind of gradients, and the physical mechanism is analyzed through the gradon modes. These results have potential applications in designing nanostructured plasmonic devices.
• Scale-free property of local-world networks and their community structures

  Shuhei Furuya, Kousuke Yakubo

  PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 389 (24) 5878 - 5886 0378-4371 2010/12 [Refereed][Not invited]
   

  The scale-free property and community structures of complex networks formed by local events have been studied theoretically, numerically, and empirically. We showed analytically and numerically that the degree distribution function P(k) of the local-world evolving network exhibits a crossover from an exponential to power-law form by increasing the local-world size M. For M much larger than the crossover local-world size M-co, the distribution function P(k) has a power-law form for any degree k(>> 1). Below M-co, however, P(k) obeys a power law for 1 << k << k(co) and decays exponentially for k >> k(co). The crossover size M-co and the crossover degree k(co) have been also elucidated. In addition, we constructed the drug prescription network (DPN) as a real local-world network, in which the local-world subsets are definitely specified, to reveal how the local-world nature affects properties of real-world networks. We found that the community structure of the DPN strongly correlates with the local worlds. Crown Copyright (c) 2010 Published by Elsevier B.V. All rights reserved.
• Reciprocal relation between the fractal and the small-world properties of complex networks

  F. Kawasaki, K. Yakubo

  PHYSICAL REVIEW E 82 (3) 36113  1539-3755 2010/09 [Refereed][Not invited]
   

  The fractal and the small-world properties of complex networks are systematically studied both in the box-covering (BC) and the cluster-growing (CG) measurements. We elucidate that complex networks possessing the fractal (small-world) nature in the BC measurement are always fractal (small world) even in the CG measurement and vice versa, while the fractal dimensions dB by the BC measurement and d(C) by the CG measurement are generally different. This implies that two structural properties of networks, fractality and small worldness, cannot coexist in the same length scale. These properties can, however, crossover from one to the other by varying the length scale. We show that the crossover behavior in a network near the percolation transition appears both in the BC and CG measurements and is scaled by a unique characteristic length xi.
• Statistical properties of weighted complex networks characterized by metaweights

  Shuhei Furuya, Kousuke Yakubo

  PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 389 (6) 1265 - 1272 0378-4371 2010/03 [Refereed][Not invited]
   

  We propose several characterizations of weighted complex networks by incorporating the concept of metaweight into the clustering coefficient, degree correlation, and module decomposition. These incorporations make it possible to describe weighted networks depending on how strongly we emphasize weights. Using some applications to real-world weighted networks, we demonstrate that the proposed approach provides rich information that was inaccessible by previous analyses such as the degree correlation for a specific magnitude of weights or the community structure under controlling the importance of roles of the topology and weights. (C) 2009 Elsevier B.V. All rights reserved.
• Fluctuations of the Order Parameter in Critical Complex Networks

  Mutsumi Mitobe, Kousuke Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 78 (12) 124002  0031-9015 2009/12 [Refereed][Not invited]
   

  The generalized Gumbel distribution function (GGDF) has been conjectured to describe fluctuating order parameters of a large class of finite critical systems. We study probability distribution functions (PDFs) of resealed order parameters in finite complex networks near their critical points to clarify whether this conjecture holds for any critical system. Our numerical results show that the PDF for fitness-model networks near the critical point, which has the scale-free property, cannot be described by the GGDF with the real parameter a equal to pi/2 while the PDF for non-scale-free Erdos-Renyi random Graphs obeys it. We also discuss the origin of the discrepancy with the GGDF in the scale-free network.
• Energy Relaxation in Damped Two-Dimensional Graded Elastic Lattices

  Mingjie Zheng, Jun Jun Xiao, Kousuke Yakubo, Kin Wah Yu

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 78 (12) 124603  0031-9015 2009/12 [Refereed][Not invited]
   

  We have studied the relaxation rate of vibrational modes in damped two-dimensional graded mass lattices. The relaxation rate spectrum in the weak damping limit can be obtained analytically through a perturbation theory based on the semiclassical quantum analogue envelope function. We found dip or peak structures on the relaxation rate spectrum. The dip or peak structures can be described quantitatively by the asymptotic behavior of relaxation rate at the transition frequencies. The frequency dependence of the relaxation rate is qualitatively explained by the mode patterns of gradon modes. The validity of the analytic results is confirmed by numerical solution with weak damping. In the strong damping case, we need to retain higher-order perturbations. These results can be applied to the energy relaxation in analogous systems.
• Distribution of Fluctuating Fractal Dimensions of Finite Critical Systems

  Mutsumi Mitobe, Kousuke Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 78 (7) 74006  0031-9015 2009/07 [Refereed][Not invited]
   

  General form of the probability distribution function (PDF) of the rescaled fractal dimension characterizing spatial structures of local order parameters in finite but large systems near the critical point is derived. To obtain the PDF, we assume that (i) sample-to-sample fluctuations of global order parameters are described by the generalized Gumbel distribution function, which is known to be valid for many of long-range correlated systems such as critical systems and (ii) spatial structures of local order parameters are always fractal at the critical point. From the obtained PDF, it is elucidated that fluctuations of fractal dimensions do not exhibit a universal character in contrast to the case of fluctuating global order parameters. In addition, we perform numerical calculations of the PDF for two-dimensional percolation systems near the critical concentration and confirm that the analytically calculated PDF well describes numerical results. We also discuss the influence of non-fractal critical clusters neglected under the assumption (ii).
• Finite size effects in infinitely large electronic systems with correlated disorders

  Shinya Nishino, Kousuke Yakubo, Hiroyuki Shima

  PHYSICAL REVIEW B 79 (3) 33105  1098-0121 2009/01 [Refereed][Not invited]
   

  We investigate localization properties of one-dimensional electronic systems with long-range correlated disorders characterized by a power-law spectral density. An abrupt change from extended to gradon states is found to occur in individual samples independently of system sizes. This abrupt change differs from the ordinary Anderson transition in the sense that the former accompanies strong sample fluctuations that remain significant even in the thermodynamic limit. We further observe that sample-averaged quantities such as the inverse participation ratio and the level-spacing distribution exhibit nontrivial crossover behaviors from extended states to gradon states.
• Generalized strength of weighted scale-free networks

  S. Furuya, K. Yakubo

  PHYSICAL REVIEW E 78 (6) 66104  2470-0045 2008/12 [Refereed][Not invited]
   

  An analysis to describe statistical properties of weighted complex networks is proposed. Effective structures of weighted networks depend on how strongly weights w are paid attention or which weights are relevant to the network problem. Defining the metaweight w(q) with a real parameter q, we characterize systematically weighted complex networks depending on the level of importance of weights. It is found that power-law distribution functions R-q[s(q)] of metastrengths s(q) defined by s(i)(q)=Sigma(j)w(ij)(q), where i and j denote node indices for any q are characterized by only three exponents if the weight distribution is independent of network topology. We also examine the validity of our analytical arguments and the meaning of power-law forms of R-q[s(q)] for different q values by illustrating some examples.
• Generalized strength of weighted scale-free networks

  S. Furuya, K. Yakubo

  Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 78 (6) 1539-3755 2008/12/01 [Refereed][Not invited]
   

  An analysis to describe statistical properties of weighted complex networks is proposed. Effective structures of weighted networks depend on how strongly weights w are paid attention or which weights are relevant to the network problem. Defining the metaweight wq with a real parameter q, we characterize systematically weighted complex networks depending on the level of importance of weights. It is found that power-law distribution functions Rq [s (q)] of metastrengths s (q) defined by si (q) = of metastrengths sq defined by denote node indices for any q are characterized by only three exponents if the weight distribution is independent of network topology. We also examine the validity of our analytical arguments and the meaning of power-law forms sq for different values by illustrating some examples. © 2008 The American Physical Society.
• Anomalous size dependence of inverse participation ratio of eigenfunctions in graded elastic lattices

  Mingjie Zheng, Masaki Goda, Ksuke Yakubo, Kin Wah Yu

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 77 (9) 94601  0031-9015 2008/09 [Refereed][Not invited]
   

  We have studied the inverse participation ratio (IPR) denoted by P-1 of vibrational modes in one-dimensional graded elastic chains. The size dependence of IPR can be shown to derive from a quantum interpretation of vibrational modes. The quantum analogue of peculiar vibrational modes (gradons) to graded systems is established for the hump structure of the gradon front via the fact that the probability of a quantum particle is inversely proportional to its velocity. In this way, the envelope function can be determined analytically, and matches the mode pattern quite well. We find that the IPR exhibits an anomalous size (N) dependence and can be captured accurately by the relation: NP-1 = C-1 log N + C-2 where C, and C, are constants. This interpretation is important in understanding a wide variety of properties of graded systems.
• Anomalously localised states at the Anderson transition

  K. Yakubo, H. Obuse

  EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 161 233 - 247 1951-6355 2008/07 [Refereed][Not invited]
   

  Non-multifractal critical wave functions at the Anderson transition are numerically investigated for the SU(2) model belonging to the two-dimensional symplectic class. These states can be regarded as anomalously localised states (ALS) at criticality. Giving a quantitative definition of ALS, it has been revealed that the probability to find ALS increases with the system size and remains at a finite value even in the thermodynamic limit. The most probable, namely typical, critical states have the multifractal nature, while its probability measure is zero. In order to understand how ALS affect critical properties in infinite systems, we studied the distribution of the correlation dimension D-2 and the nearest-neighbour level spacing distribution P(s) by paying attention to ALS. Results show that the influence of ALS to these distribution functions is limited. This is because the spatial distribution of amplitudes in tail regions of ALS exhibits multifractality as in the case of typical critical wave functions.
• Topological aspects of excitons in artificial structure

  Masami Kumagai, Akihito Taguchi, Toshihide Takagahara, Takahisa Ohno, Kousuke Yakubo

  SOLID STATE COMMUNICATIONS 145 (3) 154 - 158 0038-1098 2008/01 [Refereed][Not invited]
   

  The exciton properties of thin nanotube structures are investigated theoretically. Anisotropic size dependencies have been found in the exciton binding energy, the kinetic energy for the relative motions of an electron and a hole, and the wavefunction. These anisotropies arise from the different boundary conditions in the tube-length and circumferential directions, namely, the topological features of nanotubes. We also found that it is possible to change the topology of exciton wavefunctions by varying the tube-length and the tube-radius. These findings suggest that the optical properties of nanotubes such as oscillator strength or nonlinear susceptibilities can be controlled by tuning the structural parameters, thus yielding a novel guiding principle for designing optical functional materials. (c) 2007 Elsevier Ltd. All rights reserved.
• Vibrational excitations in graded elastic chains

  J. J. Xiao, K. Yakubo, K. W. Yu

  INTERNATIONAL JOURNAL OF MODERN PHYSICS B 21 (23-24) 4184 - 4189 0217-9792 2007/09 [Refereed][Not invited]
   

  We study vibrational excitations in linearly graded materials and/or systems. Graded systems demonstrate a unique spectrum and mode profiles, resulting in a new type of localization-delocalization transition. The nature of gradients can confine certain vibrational excitations, and redistribute them spatially. These features are contrasted to the two extreme cases of inhomogeneous system, i.e., periodically modulated system and randomly disordered system, We show in detail vibrational normal modes sustained by one dimensional graded force constant and graded mass networks, in particular, a unusual kind of modes called gradons. We propose an approach to study vibrational modes in a grades elastic system with the help of a series of homogeneous systems. Using this approach, we elaborate the features of the elastic gradons and the phonon-gradon transition.
• Coupled plasmon modes and their localization in graded plasmonic chains

  J. J. Xiao, K. Yakubo, K. W. Yu

  PHYSICA B-CONDENSED MATTER 394 (2) 208 - 212 0921-4526 2007/05 [Refereed][Not invited]
   

  Plasmonic waves occur in the subwavelength scale with transverse confinement below the diffraction limit. In this work, we report results of longitudinal localization-delocalization transitions of coupled plasmon modes in graded chains of metallic nanodots. Two graded models are studied: graded index of refraction in the host medium and incremental spacing between the nanoparticles. The coupled plasmon modes in these graded systems exhibit strong localization, showing a tunable passband in finite size systems. These localized modes survive in presence of weak loss in the nanodots. To understand the localization mechanism, we construct equivalent systems of one-dimensional coupled harmonic oscillators, whose coupling strength or masses are gradually varied from one end to the other, with additional on-site potentials. Confining and transmitting electromagnetic energy in these structures may pave new way for many fruitful applications in plasmonics. (c) 2007 Elsevier B.V. All rights reserved.
• Confined vibrational normal modes in graded elastic networks: Gradons

  K. Yakubo, J. J. Xiao, K. W. Yu

  PHYSICA B-CONDENSED MATTER 394 (2) 262 - 266 0921-4526 2007/05 [Refereed][Not invited]
   

  We discuss the possibility of wave manipulation by graded materials and/or systems. In contrast to the two extreme cases of inhomogeneous system, i.e., periodically modulated system and randomly disordered system, graded system demonstrates a unique way to control wave, resulting in a new type of localization-delocalization transition, which can confine certain vibrational excitations, and redistribute them spatially. We report in detail vibrational normal modes sustained by one-dimensional graded force constant and graded mass networks, in particular, an unusual kind of modes called gradons. By examining the mode characteristics, we put forth an approach to examine the excitation modes in a graded elastic system with the help of a series of homogeneous systems. By this approach, we elaborate the features of the elastic gradons and the phonon-gradon transition. As very useful results, we analytically present the explicit density of states of linearly graded networks in one dimension. (c) 2007 Elsevier B.V. All rights reserved.
• Non-fractal critical clusters at the percolation transition

  K. Yakubo, M. Mitobe

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 76 (3) 34004  0031-9015 2007/03 [Refereed][Not invited]
   

  We study statistical fluctuations of fractality of infinitely spanning clusters in bond percolation systems at the percolation threshold p, formed on two-dimensional square lattices by introducing a quantity Gamma representing non-fractality of a given cluster. The distribution function of Gamma reveals that most of critical clusters do not take fractal structures in the thermodynamic limit while typical structure in all possible clusters having various values of Gamma is fractal (Gamma = 0). The existence of non-fractal critical clusters is also supported by the system size dependence of the strength of the fluctuations in fractal dimensions of clusters. It is plausible that such a large fluctuation in fractality is a common feature of disorder-induced critical phenomena.
• Variety of normal modes and their transition behaviors in graded elastic networks: Square networks with a diagonal gradient

  Jun Jun Xiao, Kousuke Yakubo, Kin Wah Yu

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 76 (2) 24602  0031-9015 2007/02 [Refereed][Not invited]
   

  We study vibrational excitations in graded elastic lattices modelled by coupled harmonic oscillators in a square lattice, in which the force constants or the vibrating masses vary along a diagonal direction, rather than along an orthogonal direction [Xiao, Yakubo, and Yu: Phys. Rev. B 73 (2006) 22420 1]. As in the latter case, we identified various kinds of vibrational normal modes in these diagonally graded square lattices, namely, unbound modes, and two types of confined modes called soft (heavy) and hard (light) "gradons" which are of relatively low and high frequencies, respectively, and reside at the two opposite edges of the lattices in the gradient direction. In addition to that, we report another type of confined modes which have localization in the middle part along the gradient direction. This kind of modes appear when the transverse wave number k(s) > k(c) and approaches to the zone boundary (k(s) = pi), where k(c) is a critical wave number depending on the strength of gradient. Between k(c) < k(s) <= pi, no extended mode can be observed for whatever frequency. We name this new family of confined modes as soft-hard (light-heavy) gradons because they resemble soft (light) gradons at one end, while behaves as hard (heavy) gradons at the other end. The properties of the various normal modes and their transitions are elaborated, showing differences between orthogonally graded square lattices and diagonally graded square lattices. The underlying mechanism of the transitions is discussed with the help of a band overlapping picture.
• Global phase diagram of one-dimensional graded diatomic elastic chains: a diagrammatic approach to identifying vibrational normal modes

  J. J. Xiao, K. Yakubo, K. W. Yu

  JOURNAL OF PHYSICS-CONDENSED MATTER 19 (2) 26224  0953-8984 2007/01 [Refereed][Not invited]
   

  We study vibrational normal modes in graded diatomic chains wherein the masses m(1) of one type of atom vary linearly with the gradient c while those of the other type m(2) remain constant, in order to examine the diatomic effect on one-dimensional graded elastic chains. By means of a band overlapping picture - a convenient diagrammatic approach - we found six distinct kinds of vibrational mode, four of which are localized and two extended. Depending on their characteristics, we are also able to categorize these modes into acoustic and optical modes. Furthermore, investigating transitions among these rich normal modes we construct the global phase diagrams of vibrational modes in the omega-c space. All results are verified by numerical calculations in finite size systems.
• Localized vibrations in graded lattices: Gradons

  K. Yakubo, J. J. Xiao, K. W. Yu

  12TH INTERNATIONAL CONFERENCE ON PHONON SCATTERING IN CONDENSED MATTER (PHONONS 2007) 92 1742-6588 2007 [Refereed][Not invited]
   

  We have studied localized vibrational modes in graded elastic lattices in which vibrating masses or nearest-coupling force constants vary linearly in a uniaxial direction. We found localized modes, called gradons, whose characteristics axe peculiar to graded systems and are qualitatively different from localized states due to diffusive scattering in disordered media and confined excitations trapped by impurity potentials. The spectral properties and features of mode profiles of gradons axe presented in a simple one-dimensional graded chain. In addition, it is shown that a variety of gradons can be excited in graded diatomic chains. We also demonstrate that a band overlapping picture is efficient to understand the variety of gradon modes and their transitions to extended phonon modes.
• Dispersion and transitions of dipolar plasmon modes in graded plasmonic waveguides

  J. J. Xiao, K. Yakubo, K. W. Yu

  APPLIED PHYSICS LETTERS 89 (22) 221503  0003-6951 2006/11 [Refereed][Not invited]
   

  Coupled plasmon modes are studied in graded plasmonic waveguides, which are periodic chains of metallic nanoparticles embedded in a host with gradually varying refractive indices. The authors identify three types of localized modes called "light," "heavy," and "light-heavy" plasmonic gradons outside the passband, according to various localizations. The authors also demonstrate different transitions among extended and localized modes when the interparticle separation d is smaller than a critical d(c), whereas the three types of localized modes occur for d > d(c), with no extended modes. The transitions can be explained with phase diagrams constructed for the lossless metallic systems. (c) 2006 American Institute of Physics.
• Topological factors in placental surface arteries correlate with neonatal birth weight.

  Yamada H, Shimada S, Nishida R, Yakubo K

  THE HOKKAIDO JOURNAL OF MEDICAL SCIENCE 81 (5) 365 - 370 0367-6102 2006/09 [Refereed][Not invited]
  
• Optical switching in graded plasmonic waveguides

  J. J. Xiao, K. Yakubo, K. W. Yu

  APPLIED PHYSICS LETTERS 88 (24) 241111  0003-6951 2006/06 [Refereed][Not invited]
   

  A mechanism of longitudinal confinement of optical energy via coupled plasmon modes is proposed in chains of noble metal nanoparticles embedded in a graded dielectric medium, which is analogous to the confinement of electrons in semiconductor quantum wells. In these systems, one can control the transmission of optical energy by varying the graded refractive index of the host medium or the separation between the nanoparticles to realize the photonic analog of electronic transistors. Possible passband tunability by nanoparticle spacing and modulation of the refractive index in the host medium have been presented explicitly and compared favorably with numerical calculations.
• Harmonic vibrations in two-dimensional graded elastic networks: Variety of normal modes and their transitions

  J. J. Xiao, K. Yakubo, K. W. Yu

  PHYSICAL REVIEW B 73 (22) 224201  2469-9950 2006/06 [Refereed][Not invited]
   

  We study vibrational excitations in graded elastic networks modeled by coupled harmonic oscillators in a square lattice, in which the force constants or the vibrating masses can vary along one direction, i.e., the gradient direction. It turns out that the two-dimensional network under study can be reduced to a set of effective one-dimensional graded chains [Phys. Rev. B 73, 054201 (2006)] with additional on-site potentials. We identify various kinds of vibrational normal modes in these networks with graded force-constant (mass), namely, unbound modes and two types of confined modes called soft (heavy) and hard (light) "gradons" which reside at the two opposite edges of the network in the gradient direction. The transitions from gradons to unbound modes occur at specific frequencies omega(c1)(k(s)) and omega(c2)(k(s)) for each corresponding wave number k(s) in the transverse direction. While above the maximum of omega(c2)(k(s)), pure hard (light) gradons exist, there is severe mixing of nondegenerate phonons and gradons below this frequency, showing intriguing zigzag inverse participation ratio. It is very interesting to see such unusual excitation modes that have adjacent eigenvalues but possess quite different spatial extents. The results reduce to the previously obtained one-dimensional results for k(s)=0. The method is quite general and applicable to three-dimensional elastic networks. We conclude with discussions on how these new gradon modes may affect the macroscopic properties of graded solids. Our results can also be applied to analogous systems with graded character.
• Harmonic vibrational excitations in graded elastic networks: Transition from phonons to gradons

  JJ Xiao, K Yakubo, KW Yu

  PHYSICAL REVIEW B 73 (5) 54201  1098-0121 2006/02 [Refereed][Not invited]
   

  We have identified a different type of transition from extended to localized vibrational states in one-dimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearest-coupling force constants vary linearly along the chain. We found that the delocalization transition occurs at the maximum frequency of the corresponding homogeneous chain, which is in a continuous single band. Although each state in the localized phase, called gradon, can be regarded as an impurity localized mode, the localization profile is clearly distinct from usual impurity modes or the Anderson localized modes. We also argue how gradons may affect the macroscopic properties of graded systems. Our results can provide insights into many analogous systems with graded characters.
• Critical Level Statistics for Anomalously Localized States at the Anderson Transition Point and Their Multifractality

  K. Yakubo, H. Obuse

  AIP Conference Proceedings 0094-243X 2006
• Harmonic vibrations in two-dimensional graded elastic networks: Variety of normal modes and their transitions

  J. J. Xiao, K. Yakubo, K. W. Yu

  Physical Review B - Condensed Matter and Materials Physics 73 (22) 1098-0121 2006 [Refereed][Not invited]
   

  We study vibrational excitations in graded elastic networks modeled by coupled harmonic oscillators in a square lattice, in which the force constants or the vibrating masses can vary along one direction, i.e., the gradient direction. It turns out that the two-dimensional network under study can be reduced to a set of effective one-dimensional graded chains [Phys. Rev. B 73, 054201 (2006)] with additional on-site potentials. We identify various kinds of vibrational normal modes in these networks with graded force-constant (mass), namely, unbound modes and two types of confined modes called soft (heavy) and hard (light) "gradons" which reside at the two opposite edges of the network in the gradient direction. The transitions from gradons to unbound modes occur at specific frequencies ωc1 (ks) and ωc2 (ks) for each corresponding wave number ks in the transverse direction. While above the maximum of ωc2 (ks), pure hard (light) gradons exist, there is severe mixing of nondegenerate phonons and gradons below this frequency, showing intriguing zigzag inverse participation ratio. It is very interesting to see such unusual excitation modes that have adjacent eigenvalues but possess quite different spatial extents. The results reduce to the previously obtained one-dimensional results for ks =0. The method is quite general and applicable to three-dimensional elastic networks. We conclude with discussions on how these new gradon modes may affect the macroscopic properties of graded solids. Our results can also be applied to analogous systems with graded character. © 2006 The American Physical Society.
• Critical level statistics for anomalously localized states at the Anderson transition point and their multifractality

  K. Yakubo, H. Obuse

  LOW TEMPERATURE PHYSICS, PTS A AND B 850 1454 - + 0094-243X 2006 [Refereed][Not invited]
   

  By paying attention to anomalously localized states (ALS), we study the level-spacing distribution function P(s) at the Anderson transition. It is found that the distribution P(s) for ALS level pairs coincides with that for pairs of typical multifractal states. We also show that this remarkable result is a consequence of multifractality in tail structures of ALS.
• Non-multifractal states at the Anderson transition point

  H. Obuse, K. Yakubo

  LOW TEMPERATURE PHYSICS, PTS A AND B 850 1456 - + 0094-243X 2006 [Refereed][Not invited]
   

  We have investigated anomalously localized states (ALS) at the critical point of the Anderson transition. Nonmultifractality of ALS has been characterized by F,? calculated from the correlation function of qth moments of coarse-grained sqaured amplitudes of wave functions. It is found that the distribution function of Gamma(q) becomes broad as increasing the system size. This behavior supports our previous results for q = 2, and enables us to conclude that ALS exist at the critical point even in the thermodynamic limit.
• SQUID of a ruthenate superconductor, International Conference on Topology in Ordered Phases

  T.Matsuyama, M.Oda, Y.Asano, K.Yakubo, Y. Asano, Y. Tanaka, M. Sigrist, S. Kashiwaya

  Topology in Ordered Phases, World Scientific, Singapore 355-360  2006 [Refereed][Not invited]
  
• Spatial Structures of Anomalously Localized States in Tail Regions at the Anderson Transition

  H. Obuse, K. Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 74 242 - 245 0031-9015 2005 [Refereed][Not invited]
   

  We study spatial structures of anomalously localized states ( ALS) in tail regions at the critical point of the Anderson transition in the two-dimensional symplectic class. In order to examine tail structures of ALS, we apply the multifractal analysis only for the tail region of ALS and compare with the whole structure. It is found that the amplitude distribution in the tail region of ALS is multifractal and values of exponents characterizing multifractality are the same with those for typical multifractal wavefunctions in this universality class.
• Critical level statistics and anomalously localized states at the Anderson transition

  H Obuse, K Yakubo

  PHYSICAL REVIEW B 71 (3) 35102  1098-0121 2005/01 [Refereed][Not invited]
   

  We study the level-spacing distribution function P(s) at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution P(s) for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of P(s) to ALS is a consequence of multifractality in tail structures of ALS.
• Correlation exponent and anomalously localized states at the critical point of the Anderson transition

  H Obuse, K Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 73 (8) 2164 - 2168 0031-9015 2004/08 [Refereed][Not invited]
   

  We study the box-measure correlation function of quantum states at the Anderson transition point with taking care of anomalously localized states (ALS). By eliminating ALS from the ensemble of critical wavefunctions, we confirm, for the first time, the scaling relation z(q) = d + 2tau(q) - tau(2q) for a wide range of q, where q is the order of box-measure moments and z(q) and tau(q) are the correlation and the mass exponents, respectively. The influence of ALS to the calculation of z(q) is also discussed.
• Anomalously localized states and multifractal correlations of critical wave functions in two-dimensional electron systems with spin-orbital interactions

  H. Obuse, K. Yakubo

  Physical Review B - Condensed Matter and Materials Physics 69 (12) 1550-235X 2004/03/02 [Refereed][Not invited]
   

  Anomalously localized states (ALS) at the critical point of the Anderson transition are studied for the SU(2) model belonging to the two-dimensional symplectic class. Giving a quantitative definition of ALS to clarify their statistical properties, the system-size dependence of a probability to find ALS at criticality is presented. It is found that the probability increases with the system size and ALS exist with a finite probability even in an infinite critical system, though the typical critical states are kept to be multifractal. This fact implies that ALS should be eliminated from an ensemble of critical states when studying critical properties from distributions of critical quantities. As a demonstration of the effect of ALS on critical properties, we show that the distribution function of the correlation dimension D2 of critical wave functions becomes a δ function in the thermodynamic limit only if ALS are eliminated. © 2004 The American Physical Society.
• Anomalously localized states and multifractal correlations of critical wave functions in two-dimensional electron systems with spin-orbital interactions

  H Obuse, K Yakubo

  PHYSICAL REVIEW B 69 (12) 125301  2469-9950 2004/03 [Refereed][Not invited]
   

  Anomalously localized states (ALS) at the critical point of the Anderson transition are studied for the SU(2) model belonging to the two-dimensional symplectic class. Giving a quantitative definition of ALS to clarify their statistical properties, the system-size dependence of a probability to find ALS at criticality is presented. It is found that the probability increases with the system size and ALS exist with a finite probability even in an infinite critical system, though the typical critical states are kept to be multifractal. This fact implies that ALS should be eliminated from an ensemble of critical states when studying critical properties from distributions of critical quantities. As a demonstration of the effect of ALS on critical properties, we show that the distribution function of the correlation dimension D-2 of critical wave functions becomes a delta function in the thermodynamic limit only if ALS are eliminated.
• Quantized charge transport in adiabatic pumping by a driven double delta-barrier

  K Yakubo

  SUPERLATTICES AND MICROSTRUCTURES 34 (3-6) 259 - 262 0749-6036 2003/09 [Refereed][Not invited]
   

  We investigate the condition that the charge carried by quantum parametric pumping per cycle is quantized in units of the electron charge e and the role of adiabaticity in charge quantization. Using a driven double-delta-potential model and a Floquet scattering approach, it is found that the quantization phenomenon occurs only at very low frequencies of the oscillating potential and adiabaticity of the potential modulation is crucial for quantization. (C) 2004 Elsevier Ltd. All rights reserved.
• Critical transport and anomalously localized states at the Anderson transition

  H Obuse, K Yakubo

  SUPERLATTICES AND MICROSTRUCTURES 34 (3-6) 557 - 561 0749-6036 2003/09 [Refereed][Not invited]
   

  The effect of anomalously localized states (ALS) for electron transport at the critical point of the Anderson transition is numerically investigated for two-dimensional symplectic systems. Defining ALS quantitatively, it is found that a probability of finding ALS at criticality increases with the system size, and saturates in an infinite system. This remarkable feature influences transport properties at criticality. (C) 2004 Elsevier Ltd. All rights reserved.
• AC current due to photon-assisted tunneling in driven mesoscopic systems

  K Yakubo, JI Ohe

  PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 18 (1-3) 97 - 98 1386-9477 2003/05 [Refereed][Not invited]
   

  Photon-assisted AC transport through coherently driven mesoscopic systems has been studied by employing a transfer-matrix method. For a driven double-barrier system as a simple model of a quantum dot, we show that the AC current due to quantum interference between different sideband states depends on wavenumbers of electrons and exhibits sideband peaks. We also suggest that such AC currents can be observed in a driven mesoscopic ring which provides a novel type of photon-assisted tunneling. (C) 2003 Elsevier Science B.V. All rights reserved.
• Non-universal exponents at the Anderson transition

  H Obuse, K Yakubo

  PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 18 (1-3) 276 - 277 1386-9477 2003/05 [Refereed][Not invited]
   

  Fluctuations of the correlation dimension D-2 describing multifractal properties of critical wavefunctions at the two- and three-dimensional Anderson transition points are studied by employing the forced-oscillator method and the box-counting procedure. We show that the width of the distribution function of D-2 over disorder realizations remains finite even in the thermodynamic limit. Similar results are obtained for the exponent alpha characterizing quantum diffusion at criticality. These imply that exponents defined at the critical point may not be universal. It is also shown that the scaling relation D-2 = dalpha (d is the spatial dimension) does not hold for individual samples, but is the case in a statistical sense. (C) 2003 Elsevier Science B.V. All rights reserved.
• Numerical study of the sideband quenching in driven mesoscopic systems

  JI Ohe, K Yakubo

  PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 18 (1-3) 333 - 334 1386-9477 2003/05 [Refereed][Not invited]
   

  Coherent electron transport through a system driven by a time-varying potential is theoretically studied by employing a transfer-matrix method which enables us to investigate not only DC but also AC transport of dynamical mesoscopic systems. It has been found that AC currents in a driven double-barrier system become minimum at certain values alpha* of the strength of the time-varying potential, as in the case of the sideband quenching of DC transport. The nature of the AC quenching is, however, different from the DC one. (C) 2003 Elsevier Science B.V. All rights reserved.
• Persistent currents in Mobius strips

  K Yakubo, Y Avishai, D Cohen

  PHYSICAL REVIEW B 67 (12) 125319  1098-0121 2003/03 [Refereed][Not invited]
   

  The relation between the geometry of a two-dimensional sample and its equilibrium physical properties is exemplified here for a system of noninteracting electrons on a Mobius strip. Dispersion relation for a clean sample is derived and its persistent current under moderate disorder is elucidated, using statistical analysis pertinent to a single sample experiment. The flux periodicity is found to be distinct from that in a cylindrical sample, and the essential role of disorder in the ability to experimentally identify a Mobius strip is pointed out.
• Fluctuations of the correlation dimension of critical wavefunctions in two-dimensional symplectic systems

  Kousuke Yakubo, Hideaki Obuse

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 72 143 - 144 0031-9015 2003/02 [Refereed][Not invited]
  
• Acceleration of the forced oscillator method and its application to a model for glasses

  H Shima, K Yakubo, T Nakayama

  PHYSICA B-CONDENSED MATTER 316 521 - 523 0921-4526 2002/05 [Refereed][Not invited]
   

  The forced oscillator method is a powerful algorithm to calculate physical quantities of the system described by very large Hamiltonian matrices. The efficiency of this algorithm is greatly enhanced by combining the fast time-evolution method. The article gives a description of these numerical methods, including its applications to a model for three-dimensional network glasses. (C) 2002 Elsevier Science B.V. All rights reserved.
• The forced oscillator method incorporating the fast time-evolution algorithm

  H Shima, H Obuse, K Yakubo, T Nakayama

  COMPUTER PHYSICS COMMUNICATIONS 142 (1-3) 418 - 423 0010-4655 2001/12 [Refereed][Not invited]
   

  The forced oscillator method (FOM) is a powerful algorithm to calculate linear response functions of quantum systems represented by very large Hamiltonian matrices. We demonstrate the efficiency of the FOM by applying for the calculation of the ac conductivity sigma(omega) for two-dimensional electron systems with spin-orbit interactions. for which conventional numerical methods are inoperative. It is shown that the efficiency of the FOM is greatly enhanced by combining the fast time-evolution method. (C) 2001 Elsevier Science B.V. All rights reserved.
• Quantum transport in long-range random magnetic fields

  H Shima, K Yakubo, T Nakayama

  COMPUTER PHYSICS COMMUNICATIONS 142 (1-3) 424 - 428 0010-4655 2001/12 [Refereed][Not invited]
   

  The frequency dependence of the ac conductivity for a two-dimensional electron system subject to a long-range random magnetic field (RMF) with zero mean is numerically investigated. It is found that the ac conductivity (Tuv) increases in the frequency regime lower than a crossover frequency omega(c) and linearly decreases for to omega much greater than omega(c). The crossover frequency is governed by the localization length of the electron eigenstate at the Fermi energy. These facts indicate that quantum-interference effects are crucial for ac transport in the long-range RMF in conflict with the recent analytical argument. (C) 2001 Elsevier Science B.V. All rights reserved.
• Transfer-matrix approach to electron transport in inhomogeneous magnetic fields

  K Yakubo

  COMPUTER PHYSICS COMMUNICATIONS 142 (1-3) 429 - 435 0010-4655 2001/12 [Refereed][Not invited]
   

  A transfer-matrix method to study quantum transport of two-dimensional (2D) electron systems subject to inhomogeneous magnetic fields has been developed. This method enables us to calculate conductance within the same order of a computing time with those of one-dimensional transfer-matrix calculations. This is because the present method does, not involve any diagonalization procedure, while a conventional transfer-matrix technique for 2D systems requires to diagonalize the Hamiltonian for thin strips in the system, which consumes a long computing time. Using this method, we calculate conductances of 2D electrons in periodically modulated and random magnetic fields. (C) 2001 Elsevier Science B.V. All rights reserved.
• ac current in nonequilibrium mesoscopic systems

  J Ohe, K Yakubo

  COMPUTER PHYSICS COMMUNICATIONS 142 (1-3) 436 - 441 0010-4655 2001/12 [Refereed][Not invited]
   

  A transfer-matrix method to study ac transport in harmonically driven mesoscopic electron systems has been developed. This method makes it possible to calculate, without consuming a large amount of computing time and memory space. nonlinear ac currents in nonequilibrium systems by means of transmission and reflection amplitudes of electrons through sideband states produced by the oscillating potential. We also discuss a way to take a thermal average of the ac current at a finite temperature under a finite dc-bias voltage. Simple applications of this method exhibit the efficiency of this numerical technique. (C) 2001 Elsevier Science B.V. All rights reserved.
• Transfer-matrix formalism for 2D quantum transport in long-range inhomogeneous magnetic fields

  K Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 70 (11) 3331 - 3341 0031-9015 2001/11 [Refereed][Not invited]
   

  A transfer-matrix method is found to be an efficient numerical technique to study quantum transport of two-dimensional (2D) electron systems subject to long-range inhomogeneous magnetic fields. In contrast to conventional transfer-matrix techniques for 2D transport, the method developed in this paper does not require any diagonalization procedure. It is, therefore, possible to calculate the conductance and the current distribution within the same order of a computing time with that of a one-dimensional transfer-matrix calculation. Applying this method to several 2D electron systems in inhomogeneous magnetic fields, we demonstrate the efficiency of this method.
• Quantum-interference effect on AC transport of electrons subject to long-range random magnetic fields

  H Shima, K Yakubo, T Nakayama

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 70 (9) 2682 - 2688 0031-9015 2001/09 [Refereed][Not invited]
   

  We numerically stud's the spatial profiles of wavefunctions and the frequency dependences of the ac conductivity sigma(omega) for two-dimensional electron systems subject to long-range random magnetic fields (RMF) with zero mean. It ib found, for a weak RMF. that amplitudes of the wavefunction are almost uniformly distributed over the system, and the ac conductivity, is described by, the Drude theory Under a strong RMF, quantum states corresponding to classical snake trajectories can be strongly localized, which implies that the quantum interference along zero magnetic field contours is crucial for understanding electron transport. In this case, the conductivity sigma(omega) rapidly increases in the frequency regime lower than a crossover frequency omega (c) and decreases linearly omega much greater than omega (c). The crossover frequency is governed the localization length of the electron eigenstate at the Fermi energy.
• Quantum-interference effect on AC transport of electrons subject to long-range random magnetic fields

  H. Shima, K. Yakubo, T. Nakayama

  Journal of the Physical Society of Japan The Physical Society of Japan 70 (9) 2682 - 2688 1347-4073 2001/09/01 [Refereed][Not invited]
  
• The forced oscillator method: eigenvalue analysis and computing linear response functions

  T Nakayama, K Yakubo

  PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS 349 (3) 240 - 299 0370-1573 2001/08 [Refereed][Not invited]
   

  A review is given of the forced oscillator method (FOM), an algorithm particularly suitable to treat physical systems described by very large matrices. This scheme enables us to compute spectral densities, eigenvalues and their eigenvectors of both Hermitian and non-Hermitian matrices with high speed and accuracy, in particular when combined with the fast time-evolution method based on the Chebyshev polynomial expansion. In addition, linear response functions can be computed with high speed and accuracy in the context of the FOM. The emphasis will be on the presentation of the efficiency of the FOM for a broad range of applications with their computer source codes for the purpose of wide utility. (C) 2001 Elsevier Science B.V. All rights reserved.
• Dynamic conductivity in a 2D random magnetic field

  H Shima, K Yakubo, T Nakayama

  PHYSICA B 298 (1-4) 74 - 78 0921-4526 2001/04 [Refereed][Not invited]
   

  Th AC conductivity of a two-dimensional electron system subject to a long-range random magnetic field (RMF) with zero mean is numerically investigated. The AC conductivity sigma(omega) increases at frequencies lower than a crossover frequency omega (c), and linearly decreases for omega much greater than omega (c). The crossover frequency w, is governed by the localization length of the electron eigenstate at the Fermi energy. These results indicate that quantum interference effects are crucial for AC transport in a long-range RMF, which conflicts with a recent analytical argument. (C) 2001 Elsevier Science B.V. All rights reserved.
• Photon-assisted ac transport through quantum dots

  Ohe JI, Yakubo K

  JAPANESE JOURNAL OF APPLIED PHYSICS 公益社団法人 応用物理学会 40 (3B) 1982 - 1985 0021-4922 2001/04 [Refereed][Not invited]
   

  The ac currents through coherently driven quantum dots have been studied using a transfer-matrix method. This method enables us to calculate quantitatively the ac current of a nonequilibrium quantum system with realistic potential profiles. We show that the expected magnitude of the ac current induced by a time-varying potential is as large as that of the dc current and the photo-induced ac current can be observed by actual experiments. Amplitudes of ac current oscillate spatially, which means that the ac current depends on both frequency $\omega$ and wavenumber $q$. This is due to the fact that the ac current is induced by the interference between different sideband states. It has also been clarified that the quenching effect of ac current appears in a different manner from that of dc transport. Furthermore, we discuss a way of taking the thermal average of the ac current at a finite temperature under a finite dc-bias voltage.
• Sideband quenching in a driven double-barrier system - Scaling behavior for inhomogeneous potentials

  J Ohe, K Yakubo

  JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES & REVIEW PAPERS 40 (3B) 1986 - 1989 0021-4922 2001/03 [Refereed][Not invited]
   

  Using a transfer matrix method, we have studied the relationship between the conductance of a harmonically driven quantum dot system and the strength V-ac of the time-varying potential in both cases of (h) over bar omega not equal Delta epsilon and (h) over bar omega = Delta epsilon, where omega is the frequency of the time-varying potential and Ac is the energy distance between adjacent resonant levels of the system. In the off-resonance condition ((h) over bar omega not equal Delta epsilon). it is found that conductance dips appear in the V-ac dependence of the sideband conductance instead of the perfect sideband quenching predicted by previous works. Our results show that conductance dips corresponding to the quenching scale with omega (-1), while previous theories have suggested that the spectral weight of sideband components is scaled by omega (-2) for inhomogeneous time-varying potentials. Under the resonance condition ((h) over bar omega = Delta epsilon), our calculation shows the Rabi-type level splitting. The quenching effect of the Rabi-type splitting is also discussed.
• Low-frequency behavior of 2D electrons in a long-range random magnetic field

  H Shima, K Yakubo, T Nakayama

  PROCEEDINGS OF THE 25TH INTERNATIONAL CONFERENCE ON THE PHYSICS OF SEMICONDUCTORS, PTS I AND II 87 973 - 974 0930-8989 2001 [Refereed][Not invited]
   

  The frequency dependence of the ac conductivity of a two-dimensional electron system subject to a long-range random magnetic field (RMF) with zero mean is numerically investigated. It is found that the ac conductivity sigma(omega) increases in the frequency regime lower than a crossover frequency omega (c), and linearly decreases for omega much greater than omega (c). The crossover frequency is governed by the localization length of the electron eigenstate at the Fermi energy. These facts indicate that quantum-interference effects axe crucial for ac transport in a long-range RMF in conflict with a recent analytical argument.
• Floating of extended states in a random magnetic field with a finite mean

  K. Yakubo

  Physical Review B - Condensed Matter and Materials Physics 62 (24) 16756 - 16760 0163-1829 2000/12/15 [Refereed][Not invited]
   

  Effects of a uniform magnetic field on two-dimensional (2D) electrons subject to a random magnetic field (RMF) are studied by a multifractal scaling analysis. For sufficiently strong uniform field (B̄≫ δb), the RMF system is equivalent to a quantum Hall system (QHS), namely, the spectral density of states splits into subbands, and states only at the subband centers are extended with the localization-length exponent v= 2.31 ±0.01, where B̄ is the averaged magnetic field and δb is the characteristic amplitude of the spatially fluctuating field. In the case of B̄ ≲δb, subbands overlap each other and energies of extended states shift upwards with keeping its universality class. This behavior conflicts with a recent theoretical prediction and demonstrates that 2D systems in RMF's even with small finite means are rather close to QHS's.
• Floating of extended states in a random magnetic field with a finite mean

  K Yakubo

  PHYSICAL REVIEW B 62 (24) 16756 - 16760 1098-0121 2000/12 [Refereed][Not invited]
   

  Effects of a uniform magnetic field on two-dimensional (2D) electrons subject to a random magnetic field (RMF) are studied by a multifractal scaling analysis. For sufficiently strong uniform field ((B) over bar deltab), the RMF system is equivalent to a quantum Hall system (QHS), namely, the spectral density of states splits into subbands, and states only at the subband centers are extended with the localization-length exponent nu =2.31 +/-0.01, where B is the averaged magnetic field and deltab is the characteristic amplitude of the spatially fluctuating field. In the case of (B) over bar less than or similar to deltab, subbands overlap each other and energies of extended states shift upwards with keeping its universality class. This behavior conflicts with a recent theoretical prediction and demonstrates that 2D systems in RMF's even with small finite means are rather close to QHS's.
• Numerical study of electron transport in coherently driven double-barrier systems

  J Ohe, K Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 69 (11) 3650 - 3655 0031-9015 2000/11 [Refereed][Not invited]
   

  Quantum transport in harmonically driven double-barrier systems has been studied quantitatively by using a transfer matrix method, especially focusing our attention on the conductance as a function of the strength of the time-varying potential. In the case that the frequency w of the time-varying potential is different from Delta epsilon /h (Deltae is the energy distance between adjacent resonant levels of the system), it is found that the sideband quenching predicted previously does not occur perfectly if static and time-varying potentials hav e continuous profiles as in a realistic system. Although previous theories have suggested that the spectral weight of sideband components it; scaled by omega (-2) for inhomogenous time-varying; our results show that conductance dips corresponding to the quenching scale with omega (-1). In the case that h omega = Deltae, the Rabi-type splitting is observed. We clarified that the profile of the time-varying potential affects significantly how the resonant level splits. Furthermore, the quenching effect on the Rabi-type splitting is also discussed.
• Conductance cusp of a driven mesoscopic ring

  K Yakubo, J Ohe

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 69 (7) 2170 - 2174 0031-9015 2000/07 [Refereed][Not invited]
   

  A new type of photon-assisted tunneling (PAT) which will occur in a Marh-Zender electron interferometer with a delta-function time-varying potential is analytically predicted. In contrast to conventional PAT in Fabry-Perot electron interferometers, quite acute and cusp-like PAT signals appear in the conductance of the system. The width of thew cusp is proportional to u(1)(2)/omega where u(1) and omega are the strength and the frequency of the time-varying potential. Numerical calculations using a transfer matrix technique show that this type of PAT will be observed in actual experiments where the time-varying potential has a broader spatial profile and the temperature is finite.
• Transfer matrix approach to quantum transport in a driven mesoscopic ring

  J Ohe, K Yakubo

  PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT (138) 517 - 518 0375-9687 2000 [Refereed][Not invited]
   

  We have developed a transfer matrix method for analyzing quantum transport in harmonically driven system with spatiotemporal coherence and applied this technique to electron transport in a driven mesoscopic ring. It is predicted that novel cusps appear in the conductance as a function of the incident electron energy.
• Two-dimensional electrons in a random magnetic field with a finite mean value

  K Yakubo

  PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT (138) 525 - 526 0375-9687 2000 [Refereed][Not invited]
   

  The multifractal scaling analysis shows that; a two-dimensional electron system subject to a short-range random magnetic field with a strong mean field belongs to the same universality class with the integer quantum Hall system. It is also demonstrated, for a weak mean field, that the subband mixing pushes upwards the energy of critical states.
• Transfer matrix approach to photon-assisted quantum transport in quantum point contacts

  J Ohe, K Yakubo

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 68 (8) 2729 - 2734 0031-9015 1999/08 [Refereed][Not invited]
   

  Using a novel transfer matrix method, photon-assisted quantum transport through a quantum point contact (QPC) has been studied theoretically. Although the previous WKB theory predicts a ministep structure in the conductance of an irradiated QPC, negative experimental evidence has been reported so far. Our numerical results for a two-dimensional QPC model with realistic parameters suggest that (i) clear ministeps can he expected if the radiation field is several times stronger than that in experiments, (ii) in contrast to the WKB prediction, only ministeps in the emission side will he observed, and (iii) a wavefunction modulation by a static potential plays an important role in photon-assisted quantum transport, which has not been property evaluated in the previous theory. We also insist that a simple scenario based on the Tien-Gordon picture does not describe correctly the ministep structure.
• Finite-size scaling of multifractal wave functions: The metal-insulator transition in two-dimensional symplectic systems

  K Yakubo, M Ono

  PHYSICAL REVIEW B 58 (15) 9767 - 9772 1098-0121 1998/10 [Refereed][Not invited]
   

  A finite-size scaling analysis of wave functions near the metal-insulator transition (MIT) point has been developed, and applied to the MIT in a two-dimensional disordered electron system in the presence of spinorbit interaction. The present method has the following advantages: (i) Quantities characterizing the critical behavior, such as the critical disorder W-c or the localization exponent nu, are multiply calculated from independent scaling analyses of spatial parts with different intensities in wave functions. (ii) These quantities and the multifractality of the critical wave function are determined simultaneously. (iii)It is not necessary to treat many samples with different sizes. (iv) Much computing time is saved, and the scaling analysis can be done up to very large sizes. Using this method, we obtained W-c=5.86+/-0.04 and nu= 2.41+/-0.24 for a model of a two-dimensional symplectic system. [S0163-1829(98)08039-4].
• Transfer matrix method for a dynamical mesoscopic system

  K Yakubo

  PHYSICAL REVIEW E 57 (3) 3602 - 3610 1063-651X 1998/03 [Refereed][Not invited]
   

  A transfer matrix method for analyzing quantum transport in harmonically driven systems with spatiotemporal coherence has been developed. In such systems, the energy conservation law is violated, and transport occurs through an infinite number of sideband states. This transfer matrix method enables us to compute transmission and reflection probabilities of such dynamical mesoscopic systems without consuming a large amount of computing time and memory space. We apply this technique to photon-assisted tunneling (PAT) in a dual-gate field-effect transistor, and demonstrate the possibility of observing resonant level splittings due to the dynamical Stark effect in dual-gate PAT devices.
• High-frequency (f similar to 1 THz) studies of quantum-effect devices

  Q Hu, S Verghese, RA Wyss, T Schapers, J delAlamo, S Feng, K Yakubo, MJ Rooks, MR Melloch, A Forster

  SEMICONDUCTOR SCIENCE AND TECHNOLOGY 11 (12) 1888 - 1894 0268-1242 1996/12 [Refereed][Not invited]
   

  We have performed experimental, theoretical and simulation studies on the response of several types of antenna-coupled quantum-effect devices to high-frequency (f similar to 1 THz) radiation. The radiation-induced current in quantum point contact (QPC) devices is mainly due to heating. Our simulation study indicates that the selection rule forbids photon-excited transitions between two extended electronic states, as in the case for QPCs, if the radiation field is not tightly confined. This key understanding may explain why the observed signals in QPCs are dominated by heating. Our simulation study also shows that photon excitations can be more easily achieved in double- and multiple-barrier structures. The localized nature of the quasibound states in these structures provides the momentum spread that relaxes the selection rule. Our experimental investigation of a lateral dual-gate device has yielded radiation-induced currents with distinctively different features at different radiation frequencies. These frequency-dependent features are strong evidence that the observed radiation-induced current is due to a photonic effect that depends on the energy of individual photons.
• Localization of two-dimensional electrons in a random magnetic field

  K Yakubo, Y Goto

  PHYSICAL REVIEW B 54 (19) 13432 - 13435 0163-1829 1996/11 [Refereed][Not invited]
   

  The localization properties of a two-dimensional electron system in the presence of a random magnetic field an numerically studied by calculating directly eigenstates of large systems. Analyzing eigenstates themselves gives precise information on the localization of wave functions compared with that obtained from transport properties. The finite-size scaling analysis for quasi-one-dimensional wave functions clearly shows that the single-parameter scaling hypothesis is valid for this system and all states are localized. Furthermore, an analysis based on the multifractality of a localized wave function also supports these results.
• Simulation studies of photon-assisted quantum transport

  K Yakubo, SC Feng, Q Hu

  PHYSICAL REVIEW B 54 (11) 7987 - 7995 0163-1829 1996/09 [Refereed][Not invited]
   

  Direct numerical simulations were performed to investigate conditions for the strong effects of photon-assisted quantum transport. Transmission probabilities of incident electrons as Gaussian wave packets were calculated for single- and double-barrier structures irradiated by electromagnetic fields that were focused within a finite region xi(ac). When the period of the ac electromagnetic field is short compared with the time tau(xi ac), which is the traversal time of the electrons in the region of the applied ac field, the transmission probability can be affected by photon emission and photon absorption. The magnitude of these effects strongly depends on the width xi(ac) and the bound-state character of the electrons. These dependences can be understood from the selection rule, which results from the momentum conservation of the electron and photon system. Consequently, we have shown that photon-assisted transport over a single barrier is difficult to achieve in two-dimensional electron-gas devices due to the relatively long screening length. We have demonstrated, however, that the photon-assisted process is significantly enhanced in double-barrier devices due to quasibound-to-extended-state transitions.
• Spectral characteristics in resonators with fractal boundaries

  Y Hobiki, K Yakubo, T Nakayama

  PHYSICAL REVIEW E 54 (2) 1997 - 2004 1063-651X 1996/08 [Refereed][Not invited]
   

  Vibrations of drums with self-similar (fractal) boundaries are investigated in terms of large-scale simulations, for elucidating the characteristics of their spectral densities of states. It is found that the integrated density of states Delta I(omega) is proportional to omega(Df) (D-f the fractal dimension of the boundary) in the frequency regime higher than a characteristic frequency omega(c) with oscillating but small amplitude. The frequency omega(c) is related to the length scale characterizing the fractal boundary. We show that there exist edge modes localized near the fractal boundary under the stress-free boundary condition (Neumann condition), which vibrate at both ends of the drum with antiphase.
• Fracton decay in nonlinear fractal systems

  K Yakubo, M Nakano, T Nakayama

  PHYSICA B-CONDENSED MATTER 219-20 351 - 353 0921-4526 1996/04 [Refereed][Not invited]
   

  Anharmonic lifetimes tau(a) of fracton modes in percolating elastic networks with the fourth-order anharmonicity are numerically investigated. The results show that the frequency dependence of tau(a) drastically changes at 3 omega(c) where omega(c) is a phonon-fracton crossover frequency. The physical interpretation for the drastic change of the frequency dependence of tau(a) is given.
• Fractal drums and the Weyl-Berry-Lapidus conjecture

  Y Hobiki, K Yakubo, T Nakayama

  PHYSICA B-CONDENSED MATTER 一般社団法人 日本物理学会 219-20 354 - 356 0921-4526 1996/04 [Refereed][Not invited]
   

  We investigate the vibrational characteristics of drums with fractal perimeters, especially focusing our attention to the validity of the Weyl-Berry-Lapidus conjecture for the eigenfrequency distribution. The integrated densities of states of large-scale drums with fractal perimeters have been computed. We have confirmed that the Weyl-Beny-Lapidus conjecture should hold under the condition lambda/l much less than 1, where lambda is the wavelength of mode and I the length of the fractal segment, in addition to the condition of the high-frequency limit.
• Localization of two-dimensional electrons in a random magnetic field

  K. Yakubo, Y. Goto

  Physical Review B - Condensed Matter and Materials Physics 54 (19) 13432 - 13435 1550-235X 1996 [Refereed][Not invited]
   

  The localization properties of a two-dimensional electron system in the presence of a random magnetic field are numerically studied by calculating directly eigenstates of large systems. Analyzing eigenstates themselves gives precise information on the localization of wave functions compared with that obtained from transport properties. The finite-size scaling analysis for quasi-one-dimensional wave functions clearly shows that the single-parameter scaling hypothesis is valid for this system and all states are localized. Furthermore, an analysis based on the multifractality of a localized wave function also supports these results. © 1996 The American Physical Society.
• Simulation studies of photon-assisted quantum transport

  Kousuke Yakubo, Shechao Feng

  Physical Review B - Condensed Matter and Materials Physics 54 (11) 7987 - 7995 1550-235X 1996 [Refereed][Not invited]
   

  Direct numerical simulations were performed to investigate conditions for the strong effects of photon-assisted quantum transport. Transmission probabilities of incident electrons as Gaussian wave packets were calculated for single- and double-barrier structures irradiated by electromagnetic fields that were focused within a finite region (Formula presented). When the period of the ac electromagnetic field is short compared with the time (Formula presented), which is the traversal time of the electrons in the region of the applied ac field, the transmission probability can be affected by photon emission and photon absorption. The magnitude of these effects strongly depends on the width (Formula presented) and the bound-state character of the electrons. These dependences can be understood from the selection rule, which results from the momentum conservation of the electron and photon system. Consequently, we have shown that photon-assisted transport over a single barrier is difficult to achieve in two-dimensional electron-gas devices due to the relatively long screening length. We have demonstrated, however, that the photon-assisted process is significantly enhanced in double-barrier devices due to quasibound-to-extended-state transitions. © 1996 The American Physical Society.
• SPECTRAL DISTRIBUTION OF DRUMS WITH FRACTAL PERIMETERS - THE WEYL-BERRY-LAPIDUS CONJECTURE

  Y HOBIKI, K YAKUBO, T NAKAYAMA

  PHYSICAL REVIEW E 52 (2) R1310 - R1312 2470-0045 1995/08 [Refereed][Not invited]
   

  The Weyl-Berry-Lapidus conjecture on vibrational spectra of drums with fractal perimeters (fractal drums) is examined in terms of large-scale numerical simulations. The integrated densities of states of fractal drums with the perimeter of the Koch curve are computed by employing a powerful numerical method. It is confirmed that the Weyl-Berry-Lapidus conjecture holds in the frequency regime higher than a crossover frequency omega(c) related to the length scale characterizing the fractal boundary.
• Spectral distribution of drums with fractal perimeters: The Weyl-Berry-Lapidus conjecture

  Yutaka Hobiki, Kousuke Yakubo, Tsuneyoshi Nakayama

  Physical Review E 52 (2) R1310 - R1312 1063-651X 1995 [Refereed][Not invited]
   

  The Weyl-Berry-Lapidus conjecture on vibrational spectra of drums with fractal perimeters (fractal drums) is examined in terms of large-scale numerical simulations. The integrated densities of states of fractal drums with the perimeter of the Koch curve are computed by employing a powerful numerical method. It is confirmed that the Weyl-Berry-Lapidus conjecture holds in the frequency regime higher than a crossover frequency ωc related to the length scale characterizing the fractal boundary. © 1995 The American Physical Society.
• SPIN-WAVE DYNAMICS OF PERCOLATING HEISENBERG ANTIFERROMAGNETS

  K YAKUBO, T TERAO, T NAKAYAMA

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 63 (9) 3431 - 3441 0031-9015 1994/09 [Refereed][Not invited]
   

  The fracton dynamics of percolating Heisenberg antiferromagnets are studied in terms of a dynamic scaling argument and large-scale numerical analysis. It is shown that the spectral (or fracton) dimension for antiferromagnetic fractons, ($) over tilde d(AF), is bounded by the relation ($) over tilde d(AF)less than or equal to 1. The densities of states (DOS) are calculated for very large percolating antiferromagnets at the critical concentration p(c) formed on d=2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectral dimensions ($) over tilde d(AF) are very close to unity for any Euclidean dimension d(greater than or equal to 2). We have also calculated the DOS for percolating antiferromagnets above p(c) in order to clarify the crossover behavior from extended magnons to fractons. In addition, the dynamical structure factor S(q, omega) is investigated both analytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exponents, the dynamical exponent Z(AF) and a new exponent y. The numerical results for S(q, omega) support the validity of the single-length-scale postulate.
• NUMERICAL-METHOD FOR LARGE-SCALE NON-HERMITIAN MATRICES AND ITS APPLICATION TO PERCOLATING HEISENBERG ANTIFERROMAGNETS

  T TERAO, K YAKUBO, T NAKAYAMA

  PHYSICAL REVIEW E 50 (1) 566 - 576 1063-651X 1994/07 [Refereed][Not invited]
   

  A numerical method is developed for calculating the spectral density of states, eigenvalues, and eigenvectors of very large non-Hermitian matrices with real eigenvalues. We also present an efficient method to calculate the dynamic correlation function of the system described by non-Hermitian matrices. The effectiveness of the method is demonstrated by applying it to percolating classical Heisenberg antiferomagnets.
• SCALING PROPERTIES OF THE DYNAMICAL STRUCTURE FACTOR OF PERCOLATING HEISENBERG ANTIFERROMAGNETS

  T TERAO, K YAKUBO, T NAKAYAMA

  PHYSICAL REVIEW B 49 (17) 12281 - 12284 0163-1829 1994/05 [Refereed][Not invited]
   

  The scaling behavior of the dynamical structure factor S(q,omega) of percolating Heisenberg antiferromagnets is investigated in terms of a dynamic scaling argument and numerical calculations. It is found, based on the single-length-scaling postulate, that the asymptotic behavior of S(q,omega) can be characterized by only two exponents: the dynamic exponent z(a) and a new exponent y. This theoretical prediction is confirmed by direct numerical calculations. The values of the exponents z(a) and y are determined for the case of d = 2 percolating Heisenberg antiferromagnets.
• DYNAMICAL PROPERTIES OF FRACTAL NETWORKS - SCALING, NUMERICAL SIMULATIONS, AND PHYSICAL REALIZATIONS

  T NAKAYAMA, K YAKUBO, RL ORBACH

  REVIEWS OF MODERN PHYSICS 66 (2) 381 - 443 0034-6861 1994/04 [Refereed][Not invited]
   

  This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.
• ANTIFERROMAGNETIC FRACTON AND ITS SPECTRAL DIMENSION

  Kousuke Yakubo, Takamichi Terao, Tsuneyoshi Nakayama

  FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 1 (4) 881 - 886 0218-348X 1993/12 [Refereed][Not invited]
   

  The spectral dimensions of spin-wave fractons in percolating antiferromagnets are investigated in terms of a dynamic scaling argument and numerical simulations. It is found, by the scaling argument, that the value of the spectral dimension (d) over tilde (AF) of antiferromagnetic fractons should be less than unity for any Euclidean dimensions d(>= 2). Simulated results of (d) over tilde (AF) for d = 2, 3 and 4 percolating antiferromagnets indicate that (d) over tilde (AF)'s are very close to unity independent of Euclidean dimension d.
• DYNAMICAL STRUCTURE FACTOR OF HEISENBERG ANTIFERROMAGNETS WITH FRACTAL STRUCTURES

  Takamichi Terao, Kousuke Yakubo, Tsuneyoshi Nakayama

  FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 1 (4) 917 - 921 0218-348X 1993/12 [Refereed][Not invited]
   

  The dynamical structure factor S(q, omega) of Heisenberg antiferromagnets with random fractal structures is investigated in terms of a dynamical scaling argument. It is found that the asymptotic behavior of S(q, omega) can be characterized by the dynamic exponent z(a) and a new exponent y. We have performed numerical calculations of S(q, omega) in order to confirm its predicted scaling behaviors for d = 2 percolating antiferromagnets. The calculated values for the exponents y and z(a) are consistent with our theoretical prediction.
• SPECTRAL DIMENSION OF PERCOLATING HEISENBERG ANTIFERROMAGNETS

  K YAKUBO, T TERAO, T NAKAYAMA

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 62 (7) 2196 - 2199 0031-9015 1993/07 [Refereed][Not invited]
   

  It is found, through simulation of the density of states on a large scale, that the spectral dimensions d(AF) of percolating Heisenberg antiferromagnets take a value very close to unity independent of Euclidean dimension d. This finding is interpreted in terms of a dynamic scaling argument.
• STRONG LOCALIZATION OF PHOTONS IN APERIODIC OPTICAL WAVE-GUIDES - A NUMERICAL REALIZATION

  T NAKAYAMA, K YAKUBO, M TAKANO

  PHYSICAL REVIEW B 47 (15) 9249 - 9252 0163-1829 1993/04 [Refereed][Not invited]
   

  Numerical demonstrations of the strong localization of light are presented by illustrating aperiodic two-dimensional waveguides. For this purpose, the correspondence between the discretized form of the wave equation for light and the vibrational equation of motion for lattice dynamics is discussed in a general form. We emphasize that this mapping is useful not only to gain insight into the nature of the strong localization of light, but also to perform large-scale simulations on this phenomenon by employing an accurate numerical technique. The results will serve as a useful guide for the modeling and design of optical waveguides in which one can observe the strong localization of light.
• DYNAMIC STRUCTURE FACTOR AND ITS SINGLE-LENGTH SCALING FOR RANDOM FRACTAL STRUCTURES

  T NAKAYAMA, K YAKUBO

  PHONON SCATTERING IN CONDENSED MATTER VII 112 213 - 214 0171-1873 1993 [Refereed][Not invited]
  
• DYNAMIC STRUCTURE FACTOR AND SINGLE-LENGTH SCALING FOR RANDOM FRACTALS

  T NAKAYAMA, K YAKUBO

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 61 (8) 2601 - 2605 0031-9015 1992/08 [Refereed][Not invited]
   

  We compute the dynamic structure factors S(q, omega) for large-scale percolating networks with site numbers of the order of 10(5), by applying a novel numerical method suitable for an array-processing supercomputer. It is confirmed that the dynamic structure factors are scaled by a single characteristic length LAMBDA(omega). The scaling function h(x), where x = q-LAMBDA-(omega), behaves as x3.2 for x >> 1, and x-2.4 for x << 1. These results are argued in terms of a scaling theory for S(q, omega).
• NUMERICAL ACHIEVEMENT OF STRONG LOCALIZATION OF LIGHT IN OPTICAL WAVE-GUIDES WITH APERIODIC GRATING

  M TAKANO, K YAKUBO, T NAKAYAMA

  JAPANESE JOURNAL OF APPLIED PHYSICS PART 2-LETTERS 31 (7A) L839 - L842 0021-4922 1992/07 [Refereed][Not invited]
   

  It is demonstrated through numerical simulations that light is strongly localized in optical waveguides with an aperiodic grating. The proposed system is actually achievable by applying recent microfabrication techniques. Our results provide insight into the modeling and design of optical waveguides for observing the strong localization of light.
• LOCALIZATION EXPONENTS OF WAVES IN PERCOLATION SYSTEMS

  T TERAO, K YAKUBO, T NAKAYAMA

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 61 (7) 2173 - 2177 0031-9015 1992/07 [Refereed][Not invited]
   

  The asymptotic behavior of localized wave functions of fractons and electrons in bond-percolation systems is investigated numerically by calculating the system-size dependence of the conductance. It is found that two-dimensional (2d) fracton wave functions are superlocalized with d(phi)= 1.26+/-0.02, where d(phi) is the exponent indicating the strength of localization, while localized electronic states in 2d percolation systems decay exponentially (d(phi)= 1).
• NUMERICAL-METHOD FOR THE ANALYSIS OF OPTICAL WAVE-GUIDES

  T NAKAYAMA, M TAKANO, K YAKUBO, T YAMANAKA

  OPTICS LETTERS 17 (5) 326 - 328 0146-9592 1992/03 [Refereed][Not invited]
   

  A novel numerical method, based on the mechanical resonance to extract pure eigenmodes, is presented for calculating the modes of arbitrary-shaped optical waveguides. This method can accurately treat a system containing as many as approximately 10(6) meshes. It is demonstrated that the algorithm is useful for the analysis, modeling, and design of lossless optical waveguides.
• DYNAMIC CORRELATION-FUNCTION OF FRACTAL NETWORKS - COMPUTER EXPERIMENTS

  T NAKAYAMA, K YAKUBO

  SLOW DYNAMICS IN CONDENSED MATTER 256 279 - 282 1992 [Refereed][Not invited]
  
• ANALYSIS OF A NEW METHOD FOR FINDING EIGENMODES OF VERY LARGE LATTICE SYSTEMS

  K YAKUBO, T NAKAYAMA, HJ MARIS

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 60 (10) 3249 - 3259 0031-9015 1991/10 [Refereed][Not invited]
   

  This paper analyses a new numerical method, based on mechanical resonance to extract pure vibrational eigenmodes for very large systems. This method can be used for systems containing as many as approximately 10(6) particles, which are too large to be treated by conventional numerical methods. In addition, this algorithm can easily be vectorized for implementation on an array-processing supercomputer. A formula is given to judge the accuracy of the eigenmodes and eigenfrequencies that are found. In addition a discussion is given of how to make the most efficient choice for two key parameters entering into the algorithm, namely the driving time interval t and the number of iteractions p.
• DENSITY OF STATES OF FRACTONS ON PERCOLATING NETWORKS

  T NAKAYAMA, K YAKUBO

  PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-CHEMICAL SCIENCES 102 (5) 575 - 579 0253-4134 1990/10 [Refereed][Not invited]
  
• SUPERLOCALIZATION OF FRACTON WAVE-FUNCTIONS EXCITED ON PERCOLATING NETWORKS

  K YAKUBO, T NAKAYAMA

  PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-CHEMICAL SCIENCES 102 (5) 581 - 584 0253-4134 1990/10 [Refereed][Not invited]
  
• MISSING MODES IN THE DENSITY OF STATES OF FRACTAL NETWORKS

  K YAKUBO, E COURTENS, T NAKAYAMA

  PHYSICAL REVIEW B 42 (1) 1078 - 1081 0163-1829 1990/07 [Refereed][Not invited]
  
• CROSSOVER-BEHAVIOR FROM VECTOR TO SCALAR FRACTONS IN THE DENSITY OF STATES OF PERCOLATING NETWORKS

  K YAKUBO, K TAKASUGI, T NAKAYAMA

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 59 (6) 1909 - 1912 0031-9015 1990/06 [Refereed][Not invited]
  
• FRACTON DYNAMICS OF PERCOLATING ELASTIC NETWORKS - ENERGY-SPECTRUM AND LOCALIZED NATURE

  K YAKUBO, T NAKAYAMA

  PHYSICAL REVIEW B 40 (1) 517 - 523 2469-9950 1989/07 [Refereed][Not invited]
  
• CHARACTERISTICS OF FRACTONS - FROM SPECIFIC REALIZATIONS TO ENSEMBLE AVERAGES

  T NAKAYAMA, K YAKUBO, R ORBACH

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 58 (6) 1891 - 1894 0031-9015 1989/06 [Refereed][Not invited]
  
• DIRECT OBSERVATION OF LOCALIZED FRACTONS EXCITED ON PERCOLATING NETS

  K YAKUBO, T NAKAYAMA

  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 58 (5) 1504 - 1507 0031-9015 1989/05 [Refereed][Not invited]
  
• Fracton dynamics of percolating elastic networks: Energy spectrum and localized nature

  K. Yakubo, T. Nakayama

  Physical Review B 40 (1) 517 - 523 0163-1829 1989 [Refereed][Not invited]
   

  We have performed computer experiments on the dynamics of two- and three-dimensional (2D and 3D) percolating elastic networks with the site number N> 105. The densities of vibrational states (DOSs) for these large percolating networks as well as the mode patterns of fractons are obtained. It is confirmed, for both 2D and 3D networks, that the DOS is proportional to d-1 with d close to (4/3 in the regime above the characteristic frequency c. We could not find the notable steepness or hump in the DOS at the vicinity of a phonon-fracton crossover frequency c, i.e., our results were incompatible with the prediction by the effective-medium theory. Specific realizations of mode patterns show that the core of fracton excitations falls off sharply at their edges, and that the localized nature is quite unique. © 1989 The American Physical Society.
• ABSENCE OF THE HUMP IN THE DENSITY OF STATES OF PERCOLATING CLUSTERS

  K YAKUBO, T NAKAYAMA

  PHYSICAL REVIEW B 36 (16) 8933 - 8936 2469-9950 1987/12 [Refereed][Not invited]
  
• FRACTONS IN PERCOLATION CLUSTERS

  K YAKUBO, T NAKAYAMA

  JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS BRIEF COMMUNICATIONS & REVIEW PAPERS 26 883 - 884 0021-4922 1987 [Refereed][Not invited]
  
• KAPITZA RESISTANCE BETWEEN SINTERED METAL PARTICLES AND HE-3-HE-4 MIXTURE

  T NAKAYAMA, K YAKUBO

  JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES & REVIEW PAPERS 26 375 - 376 0021-4922 1987 [Refereed][Not invited]
  
• Absence of the hump in the density of states of percolating clusters

  K. Yakubo, T. Nakayama

  Physical Review B 36 (16) 8933 - 8936 0163-1829 1987 [Refereed][Not invited]
   

  The vibrational densities of states of two-dimensional percolating clusters with very large cluster size are investigated using a novel numerical method. It is confirmed that the fracton density of states is proportional to 13 in accord with the conjecture of Alexander and Orbach. We find that there is no notable steepness or hump in the phonon-fracton crossover region, in conflict with the prediction of the effective-medium theory. It is shown that the fracton modes are localized in "peninsulas" in percolating clusters. © 1987 The American Physical Society.

Books etc

• 複雑ネットワークとその構造

  矢久保 考介 (Single work)
  共立出版 2013/02
• Topological Aspects of Critical Systems and Networks

  YAKUBO Kousuke (Editor)
  2007/06
• Topology in Ordered Phases

  TANDA Satoshi, MATSUYAMA Toyoki, ODA Migaku, ASANO Yasuhiro, YAKUBO Kousuke (Editor)
  World Scientific Publishing Company 2006/08
• Fractal Concepts in Condensed Matter Physics

  NAKAYAMA Tsuneyoshi, YAKUBO Kousuke (Joint work)
  Springer 2003/08

Conference Activities & Talks

• Self-organized colony formation by a spatial network model  [Invited]

  YAKUBO Kousuke

  Roles of Heterogeneity in Non-equilibrium collective dynamics (RHINO 2019)  2019/07
• Detection and Analysis of Long-Range Degree Correlations in Complex Networks  [Not invited]

  FUJIKI Yuka, YAKUBO Kousuke

  StatPhys27  2019/07
• トポロジカル相の動的制御による1次元エッジ状態の輸送  [Not invited]

  藤澤有祐, 矢久保考介, 川上則雄, 小布施秀明

  日本物理学会 第74回年次大会  2019/03
• トポロジカル相を利用したエッジ状態の動的制御：等速運動する1次元エッジ状態に対するスペクトル解析と三準位モデルとの比較  [Not invited]

  FUJISAWA YUSUKE, YAKUBO KOSUKE, KAWAKAMI NORIO, OBUSE HIDEAKI

  日本物理学会 第73回年次大会  2018  東京理科大学（野田市）
• 長距離次数相関を表す指標  [Not invited]

  FUJIKI YUKA, YAKUBO KOSUKE

  日本物理学会 第73回年次大会  2018  東京理科大学（野田市）
• Degree correlations between distant nodes in complex networks  [Not invited]

  FUJIKI YUKA, YAKUBO KOSUKE

  NetSci 2018  2018  New Cap Event Center (Paris, France)
• General description of long-range degree correlations in complex networks  [Invited]

  YAKUBO KOSUKE

  The 6th International Workshop on Physics of Social Complexity (PoSCo)  2018  Pohang University of Science and Technology (Pohang, Korea)
• クラスター化されたネットワークの頑強性  [Not invited]

  YAKUBO KOSUKE, FUKUSHI KAZUYA

  日本物理学会 第72回年次大会  2017/03  大阪大学（大阪市）
• 自己組織化臨界性に基づくネットワーク形成の単純モデルの提案  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 第72回年次大会  2017/03  大阪大学（大阪市）
• トポロジカル相の接合境界が動的に変化する1次元格子モデルにおけるエッジ状態  [Not invited]

  FUJIKI YUKA, YAKUBO KOSUKE, KAWAKAMI NORIO, OBUSE HIDEAKI

  日本物理学会 2017年秋季大会  2017  岩手大学（盛岡市）
• 長距離次数相関の一般的定式化：無次数相関グラフにおける確率関数の解析  [Not invited]

  FUJIKI YUKA, YAKUBO KOSUKE

  日本物理学会 2017年秋季大会  2017  岩手大学（盛岡市）
• 自己組織化臨界動力学によるネットワークのスケールフリー性：マスター方程式からのアプローチ  [Not invited]

  YAMANE YOSHIHIRO, MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2017年秋季大会  2017  岩手大学（盛岡市）
• 自己組織化臨界性に基づくネットワーク形成とその普遍クラス  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2017年秋季大会  2017  岩手大学（盛岡市）
• 隣接ノード伝播型過負荷故障カスケードに対するネットワークの頑強性  [Not invited]

  KAMAKURA YUKI, YAKUBO KOSUKE

  日本物理学会 2017年秋季大会  2017  岩手大学（盛岡市）
• Disassortative degree mixing and fractality of scale-free networks  [Not invited]

  FUJIKI YUKA, MIZUTAKA SHOGO, YAKUBO KOSUKE

  SigmaPhi 2017  2017  Corfu Holiday Palace Hotel (Corfu, Greece)
• Fractality of Complex Networks Emerging from Self-Organized Critical Dynamics  [Not invited]

  YAKUBO KOSUKE, WATANABE AKITOMO, MIZUTAKA SHOGO

  SigmaPhi 2017  2017  Corfu Holiday Palace Hotel (Corfu, Greece)
• Long-Range Degree Correlations in Complex Networks  [Invited]

  YAKUBO KOSUKE

  The 2nd Workshop on Self-Organization and Robustness of Evolving Many-Body Systems  2017  北海道大学（札幌市）
• Non-linear Scaling in Cities  [Invited]

  YAKUBO KOSUKE

  International Workshop on Interdisciplinary Applications of Nonlinear Science  2016/11  鹿児島大学（鹿児島市）
• 自己組織化臨界ダイナミクスによるスケールフリー・ネットワークの形成  [Not invited]

  YAMANE YOSHIHIRO, MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2016年秋季大会  2016/09  金沢大学（金沢市）
• 長距離次数相関を特徴付ける同時確率と条件付き確率の一般的関係  [Not invited]

  FUJIKI YUKA, TAKAGUCHI TARO, YAKUBO KOSUKE

  日本物理学会 2016年秋季大会  2016/09  金沢大学（金沢市）
• Cascading Failures by Fluctuating Loads in Complex Networks  [Invited]

  YAKUBO KOSUKE

  The 1st Workshop on Self-Organization and Robustness of Evolving Many-Body Systems  2016/08  ホテル梅はら（神栖市）
• Cascading Failures by Fluctuating Loads in Scale-free Networks  [Not invited]

  YAKUBO KOSUKE, MIZUTAKA SHOGO

  NetSci 2016  2016/05  The K-Hotel （Seoul, Korea)
• Self-organization of Fractal Networks  [Invited]

  YAKUBO KOSUKE

  The 3rd International Workshop on Physics of Social Complexity  2016/05  Pohang University of Science and Technology (Pohang, Korea)
• (u,v)-flowerにおける隣接次数相関と長距離次数相関  [Not invited]

  FUJIKI YUKA, YAKUBO KOSUKE

  日本物理学会 第71回年次大会  2016/03  東北学院大学（仙台市）
• 複雑ネットワークにおける隣接ノード次数間のスピアマン相関係数  [Not invited]

  YAKUBO KOSUKE, FUJIKI YUKA, MIZUTAKA SHOGO

  日本物理学会 第71回年次大会  2016/03  東北学院大学（仙台市）
• 複雑ネットワークにおけるパーコレーション転移  [Invited]

  YAKUBO KOSUKE

  クロスボーダー・シンポジウム  2016/01  旭川医科大学（旭川市）
• 総負荷揺らぎを伴う過負荷故障の確率と局所負荷揺らぎのスケーリング則  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2015年秋季大会  2015/09  関西大学（吹田市）
• 負荷揺らぎに基づく故障カスケードとネットワークの頑強性  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会講演概要集(CD-ROM)  2015/03
• 自己組織化臨界的に形成されるネットワークのスモールワールド性とフラクタル性  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会講演概要集(CD-ROM)  2015/03
• 都市指標の相対成長率と偏差分布:都市個性揺らぎによる影響  [Not invited]

  SAIJO YUUSHI, YAKUBO KOSUKE

  日本物理学会講演概要集(CD-ROM)  2015/03
• 負荷揺らぎに基づく故障カスケードとネットワークの頑強性  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2015年次大会  2015/03  早稲田大学（東京都）
• 自己組織化臨界的に形成されるネットワークのスモールワールド性とフラクタル性  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会 2015年次大会  2015/03  早稲田大学（東京都）
• 都市指標の相対成長率と偏差分布：都市個性揺らぎによる影響  [Not invited]

  SAIJO YUUSHI, YAKUBO KOSUKE

  日本物理学会 2015年次大会  2015/03  早稲田大学（東京都）
• ネットワーク科学から見た感染症の流行と防疫  [Invited]

  YAKUBO KOSUKE

  第12回創成シンポジウム「感染症研究の最前線：エボラ・結核を例に」  2015/02  北海道大学（札幌市）
• A Network Model for Urban Scaling  [Invited]

  YAKUBO KOSUKE

  Cities as Organisms Scaling and Networks in Urban, Social, and Biological Systems  2015/02  University of Maribor (Maribor, Slovenia)
• 都市スケーリングと地理的ネットワーク  [Invited]

  YAKUBO KOSUKE

  高等研プロジェクト「ネットワークの科学」第２回研究集会  2014/12  国際高等研究所（木津川市）
• 自己組織化臨界性に基づく複雑ネットワークの構造形成  [Not invited]

  WATANABE AKITOMO, MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2014年秋季大会  2014/09  中部大学（春日井市）
• 複雑ネットワークのサイズと構造安定性：過負荷故障モデルからのアプローチ  [Not invited]

  MIZUTAKA SHOGO, WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会 2014年秋季大会  2014/09  中部大学（春日井市）
• 都市スケーリングとその偏差：地理的ネットワークによるモデル化  [Not invited]

  SAIJO YUUSHI, YAKUBO KOSUKE

  日本物理学会 2014年秋季大会  2014/09  中部大学（春日井市）
• 自己組織化臨界性に基づく複雑ネットワークの構造形成  [Not invited]

  WATANABE AKITOMO, MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会講演概要集  2014/08
• 複雑ネットワークのサイズと構造安定性―過負荷故障モデルからのアプローチ―  [Not invited]

  MIZUTAKA SHOGO, WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会講演概要集  2014/08
• 都市スケーリングとその偏差―地理的ネットワークによるモデル化―  [Not invited]

  SAIJO YUUSHI, YAKUBO KOSUKE

  日本物理学会講演概要集  2014/08
• 低次数領域における次数分布変化とスケールフリー・ネットワークの頑強性  [Not invited]

  KOBATAKE YUSUKE, YAKUBO KOSUKE

  日本物理学会 第69回年次大会  2014/03  東海大学（平塚市）
• 過負荷によるカスケード故障の臨界的振舞い  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 第69回年次大会  2014/03  東海大学（平塚市）
• 低次数領域における次数分布変化とスケールフリー・ネットワークの頑強性  [Not invited]

  KOBATAKE YUSUKE, MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会講演概要集  2014/03
• 過負荷によるカスケード故障の臨界的振舞い  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会講演概要集  2014/03
• Overload Network Failures: An Approach from the Random-Walk Model  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  Second Workshop on Complex Networks and their Applications  2013/12  京都テルサ（京都市）
• 触媒反応ネットワークにおけるSOCと反応回数推移の非マルコフ性  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会 2013年秋季大会  2013/09  徳島大学（徳島市）
• ランダムウォーク・モデルに基づく過負荷故障カスケードの定式化とネットワークの頑強性  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会 2013年秋季大会  2013/09  徳島大学（徳島市）
• 地理的ネットワークに基づく都市スケーリングの統一的理解  [Not invited]

  YAKUBO KOSUKE, SAIJO YUUSHI

  日本物理学会 2013年秋季大会  2013/09  徳島大学（徳島市）
• Self-organized criticality in catalytic reaction networks  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  International Workshop on Phase Transition, Critical Phenomena and Related Topics in Complex Network  2013/09  北海道大学 学術交流会館（札幌市）
• Network robustness to overload failures  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  International Workshop on Phase Transition, Critical Phenomena and Related Topics in Complex Network  2013/09  北海道大学 学術交流会館（札幌市）
• A Network Model for Urban Scaling  [Invited]

  YAKUBO KOSUKE

  International Workshop on Phase Transition, Critical Phenomena and Related Topics in Complex Network  2013/09  北海道大学 学術交流会館（札幌市）
• ランダムウォーク・モデルに基づく過負荷故障カスケードの定式化とネットワークの頑強性  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会講演概要集  2013/08
• 触媒反応ネットワークにおけるSOCと反応回数推移の非マルコフ性  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会講演概要集  2013/08
• Self-organized criticality in inhomogeneous catalytic reaction networks  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  XXV IUPAP International Conference on Statistical Physics (Statphys 25)  2013/07  Seoul National University (Seoul, Korea)
• Percolation on Scale-free Networks by Overload Failures  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  XXV IUPAP International Conference on Statistical Physics (Statphys 25)  2013/07  Seoul National University (Seoul, Korea)
• Geographical Network Model for Urban Scaling  [Not invited]

  YAKUBO KOSUKE, SAIJO YUUSHI

  XXV IUPAP International Conference on Statistical Physics (Statphys 25)  2013/07  Seoul National University (Seoul, Korea)
• 複雑ネットワークの構造とSOCの普遍クラス  [Not invited]

  WATANABE AKITOMO, YAKUBO KOSUKE

  日本物理学会2012年秋季大会  2012/09  横浜国立大学（横浜市）
• 過負荷故障に対する複雑ネットワークの堅牢性  [Not invited]

  MIZUTAKA SHOGO, YAKUBO KOSUKE

  日本物理学会2012年秋季大会  2012/09  横浜国立大学（横浜市）
• フラクタル複雑ネットワーク  [Invited]

  YAKUBO KOSUKE

  CMRU研究会 「ネットワーク科学の数理と展開」  2012/09  東北大学青葉記念会館（仙台市）
• 過負荷故障に対する複雑ネットワークの堅牢性  [Invited]

  YAKUBO KOSUKE

  SMARTプログラム 複雑ネットワーク・サマースクール  2012/09  東北大学情報科学研究科（仙台市）

MISC

• トポロジカル相の動的制御による1次元エッジ状態の輸送

  藤澤有祐, 矢久保考介, 川上則雄, 小布施秀明  日本物理学会講演概要集(CD-ROM)  74-  (1)  2019
• トポロジカル相を利用したエッジ状態の動的制御:等速運動する1次元エッジ状態に対するスペクトル解析と三準位モデルとの比較

  藤澤有祐, 矢久保考介, 川上則雄, 小布施秀明  日本物理学会講演概要集(CD-ROM)  73-  (1)  2018
• Edge states in 1D lattice models with a moving topological phase boundary

  Fujisawa Yusuke, Yakubo Kousuke, Kawakami Norio, Obuse Hideaki  Meeting Abstracts of the Physical Society of Japan  72-  (0)  1009  -1009  2017  [Not refereed][Not invited]
  
• 21aBS-5 Spearman's rank correlation coefficient between degrees of adjacent nodes in complex networks

  Yakubo K., Fujiki Y., Mizutaka S.  Meeting Abstracts of the Physical Society of Japan  71-  2992  -2992  2016
• 22pPSB-44 Allometric scaling and fluctuations of urban indicators : Influence of urban characteristics

  Saijo Y., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  70-  3075  -3075  2015
• 24pAH-6 Fractal and Small-world Properties of Networks Formed by Self-organized Critical Dynamics

  Watanabe A., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  70-  3208  -3208  2015
• 24pAH-7 Robustness of networks against cascading failures y fluctuating loads

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  70-  3209  -3209  2015
• 16pCW-6 Overload probability under the fluctuations of the total load

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  70-  2588  -2588  2015
• 29pAJ-7 Critical behavior of cascading overload failures

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  69-  (1)  349  -349  2014
• 30aPS-30 Relation between robustness of scale-free networks and their degree distributions at low connectivity

  Kobatake Y., Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  69-  (1)  366  -366  2014
• 10aAP-10 Size of Complex Networks and Their Structural Stability : An Approach from a Model with Overload Failures

  Mizutaka S., Watanabe A., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  69-  (2)  176  -176  2014
• 10aAP-11 Complex Network Formation based on Self-organized Criticality

  Watanabe A., Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  69-  (2)  176  -176  2014
• 9aAp-7 Urban Scaling and Its Deviations : Modeling by Geographical Networks

  Saijo Y., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  69-  (2)  154  -154  2014
• Robustness of complex networks against cascading overload failures modeled by random walkers

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  68-  (2)  265  -265  2013
• Geographical Network Model to Understand Urban Scaling

  Yakubo K., Saijo Y.  Meeting Abstracts of the Physical Society of Japan  68-  (2)  267  -267  2013
• Non-Markovian Character of Temporal Reaction-Number Variation in Catalytic Reaction Networks

  Watanabe A., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  68-  (2)  268  -268  2013
• 25pPSB-2 Critical behaviors and universal fluctuations of the local density of states near/at the MI transition

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  67-  (1)  340  -340  2012
• 26pBG-13 Catalytic reaction dynamics in scale-free networks

  Watanabe A., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  67-  (1)  359  -359  2012
• 20aAE-3 Robustness of Complex Networks against Overload Failures

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  67-  (2)  282  -282  2012
• 20aAE-10 Universality Class of SOC in Complex Networks

  Watanabe A., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  67-  (2)  284  -284  2012
• 26aTD-2 Crossover behavior of the return probability on a complex network near criticality

  Kawasaki F., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  66-  (1)  302  -302  2011
• 26aTD-3 Multifractality of a node density of complex networks

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  66-  (1)  302  -302  2011
• 26aTD-4 Off-diagonal complexity of random graphs

  Yakubo K., Korosak Dean  Meeting Abstracts of the Physical Society of Japan  66-  (1)  302  -302  2011
• 25pHG-7 Universal fluctuations of the order parameter at the Anderson transition

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  66-  (1)  702  -702  2011
• 23pEC-7 Complexity of random graphs: Off-diagonal complexity and criticality

  Yakubo K., Korosak Dean  Meeting Abstracts of the Physical Society of Japan  66-  (2)  277  -277  2011
• 23pEC-8 Crossover behavior of dynamical properties on a complex network near the percolation transition

  Kawasaki F., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  66-  (2)  277  -277  2011
• 23pEC-9 Multifractality of Network Topology of Fractal Complex Networks

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  66-  (2)  278  -278  2011
• 23aTL-1 Universal distribution of the order parameter at the metal-insulator transition

  Mizutaka S., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  66-  (2)  687  -687  2011
• 20aEH-4 Scale-free networks embedded in a fractal space

  Yakubo K., Korosak Dean  Meeting Abstracts of the Physical Society of Japan  65-  (1)  266  -266  2010
• 20aEH-5 Multifractality of Scale-Free Networks

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  65-  (1)  267  -267  2010
• 25aTH-4 Diffusion on fractal scale-free networks and the spectral dimension

  Kawasaki F., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  65-  (2)  278  -278  2010
• 25aTH-5 Multifractality of betweenness centrality

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  65-  (2)  278  -278  2010
• 25aTH-6 Compactness of geographical networks embedded in a fractal space

  Yakubo K., Korosak Dean  Meeting Abstracts of the Physical Society of Japan  65-  (2)  279  -279  2010
• 25aQK-3 Fractal dimensions of rewired fitness model networks at criticality

  Kawasaki F., Yakubo K.  Meeting abstracts of the Physical Society of Japan  64-  (2)  154  -154  2009/08/18
• 25aQK-4 Local-World Property and Module Structure in Drug Prescription Networks

  Furuya Shuhei, Suzuki Keita, Yakubo Kousuke  Meeting abstracts of the Physical Society of Japan  64-  (2)  154  -154  2009/08/18
• 30aTB-3 Pharmaceutical Correlation Network as a Local-world Networks

  Suzuki Keita, Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  64-  (1)  317  -317  2009
• 30aTB-4 Statistical analyses for weighted complex networks by using metaweights

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  64-  (1)  317  -317  2009
• 30pTB-1 Crossover from Fractal to Small-world Properties in Complex Networks

  Kawasaki F., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  64-  (1)  343  -343  2009
• 30pTB-2 Critical Properties of Scale-free Networks

  Oka Y., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  64-  (1)  343  -343  2009
• 30pTB-3 Universal fluctuations of the order parameter in critical complex networks

  Mitobe Mutsumi, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  64-  (1)  343  -343  2009
• 23pVC-9 Distribution of fractal dimensions and universal fluctuations in critical systems

  Mitobe Mutsumi, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  63-  (2)  282  -282  2008
• 20aPS-2 Quantum gradon states in one-dimensional electronic systems with long-range correlated disorders

  Nishino S., Yakubo K., Shima H.  Meeting Abstracts of the Physical Society of Japan  63-  (2)  589  -589  2008
• 23pWA-3 IPR Analysis of Gradons in Graded Lattices

  Yakubo K., Goda M., Zheng M., Yu K. W.  Meeting Abstracts of the Physical Society of Japan  63-  (2)  897  -897  2008
• 25pPSA-40 Criticality and Fractality of Scale-free Networks

  Oka Y., Kawasaki F., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  63-  (1)  325  -325  2008
• 23aWJ-9 Metal-insulator transition in one-dimensional electronic systems with long-range correlated disorders

  Nishino S., Yakubo K., Shima H., Nakayama T.  Meeting Abstracts of the Physical Society of Japan  63-  (1)  660  -660  2008
• 25pPSA-42 Meta-weight analysis for a scientific collaboration network

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  63-  (1)  326  -326  2008
• 25pPSA-41 Efficient fractal analysis for self-organized acquaintance networks at criticality

  Kawasaki Fumiya, Oka Yuriko, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  63-  (1)  325  -325  2008
• 21aTG-8 Localized states in graphite ribbons with disorders

  Hori Masato, Nishino Shinya, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (2)  677  -677  2007
• 23pTE-2 Biased Distribution of Localization Centers in Disordered Graded Lattices

  Yakubo K., Xiao Jun Jun, Yu Kin Wah  Meeting Abstracts of the Physical Society of Japan  62-  (2)  1004  -1004  2007
• 24aTG-6 Metal-insulator transition in two-dimensional disordered electronic systems with flat bands

  Nishino Shinya, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (2)  710  -710  2007
• 22aTL-6 Metaweight analysis for weighted complex networks

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (2)  277  -277  2007
• 18aXA-6 Various Vibrational Modes in Graded Diatomic Elastic Chains

  Yakubo K., Xiao Jun Jun, Yu Kin Wah  Meeting Abstracts of the Physical Society of Japan  62-  (1)  931  -931  2007
• 21aPS-21 Method of constructing flat bands in a tight-binding electronic system with spin-orbit coupling

  Nishino Shinya, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (1)  304  -304  2007
• 21aPS-7 Fluctuations of fractality in two dimension critical Ising clusters

  Mitobe Mutsumi, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (1)  301  -301  2007
• 21aWA-7 Generalized Strength of Weighted Scale-free Networks

  Furuya Shuhei, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  62-  (1)  297  -297  2007
• Physics and device applications of low dimensional nanostructure

  松本 和彦, 加藤 景三, 知京 豊裕, 矢久保 考介  Oyo Buturi  75-  (3)  284  -284  2006/03/10
• 28aXB-1 Anomalously Localized States at Criticality in the Three-Dimensional Disordered System

  Obuse H, Yakubo K  Meeting abstracts of the Physical Society of Japan  61-  (1)  678  -678  2006/03/04  [Not refereed][Not invited]
  
• 27pRE-2 Dielectric effect of exciton in semiconductor nanotube structures

  Kumagai Masami, Takagahara Toshihide, Ohno Takahisa, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  61-  (1)  717  -717  2006
• 25pWB-1 Optical properties of exciton in semiconductor nanotube structures

  Kumagai Masami, Takagahara Toshihide, Ohno Takahisa, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  61-  (2)  617  -617  2006
• 28pYA-3 Localized Vibrational Modes in Graded Lattice Systems : Gradons and their Properties

  Yakubo K., Xiao Jun Jun, Yu Kin Wah  Meeting Abstracts of the Physical Society of Japan  61-  (1)  940  -940  2006
• 23pYK-2 Gradon Excitations in Two-dimensional Graded lattices

  Yakubo K., Xiao Jun Jun, Yu Kin Wah  Meeting Abstracts of the Physical Society of Japan  61-  (2)  781  -781  2006
• 26aPS-24 Fluctuations of fractal dimensions in critical percolation systems

  Mitobe Mutsumi, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  61-  (2)  234  -234  2006
• Surface and biotechnology

  玉田 薫, 加藤 景三, 知京 豊裕, 矢久保 考介  Oyo Buturi  74-  (12)  1542  -1542  2005/12/10
• 20pYC-16 Topological Aspects of Wave Function Statistics at the Anderson Transition

  Obuse H, Yakubo K  Meeting abstracts of the Physical Society of Japan  60-  (2)  540  -540  2005/08/19  [Not refereed][Not invited]
  
• 21pYO-14 Non-fractal clusters in critical percolation systems and their universality

  Mitobe Mutsumi, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  60-  (2)  194  -194  2005
• 21aYC-4 Pure Spin Current due to Non-adiabatic Quantum Pumping

  Yakubo Kousuke, Morikawa Mikiya  Meeting Abstracts of the Physical Society of Japan  60-  (2)  545  -545  2005
• 21aXF-14 Excitonic process in semiconductor nanotube structures

  Kumagai Masami, Taguchi Akihito, Ohno Takahisa, Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  60-  (2)  608  -608  2005
• 非断熱過程による量子ポンピング (第6回 21世紀の境界領域研究を考えるシンポジウム)

  矢久保 考介, 森川 幹也  バウンダリ-  20-  (11)  3  -11  2004/11
• 12pYB-11 Level Statistics and Anomalously Localized States at the Anderson Transition Point

  Obuse H, Yakubo K  Meeting abstracts of the Physical Society of Japan  59-  (2)  589  -589  2004/08/25  [Not refereed][Not invited]
  
• 12pYB-12 Multifractality and Anomalously Localized States for critical wavefunctions of the Anderson Transition

  Yakubo K, Obuse H  Meeting abstracts of the Physical Society of Japan  59-  (2)  589  -589  2004/08/25  [Not refereed][Not invited]
  
• 30aYF-1 Statistical Properties of Anomalously Localized States at the Anderson Transition Point

  Obuse H, Yakubo K  Meeting abstracts of the Physical Society of Japan  59-  (1)  708  -708  2004/03/03  [Not refereed][Not invited]
  
• 27pYF-4 Quantized Charge Transport in Non-adiabatic Quantum Pumping

  Yakubo K.  Meeting Abstracts of the Physical Society of Japan  59-  (1)  674  -674  2004
• Correlations in a Multifractality of Critical Wavefunctions for a SU(2) Model

  Obuse H, Yakubo K  Meeting abstracts of the Physical Society of Japan  58-  (1)  613  -613  2003/03/06  [Not refereed][Not invited]
  
• Persistent Current in Mobius Rings

  Yakubo K., Cnhen D., Avishai Y.  Meeting Abstracts of the Physical Society of Japan  57-  (2)  553  -553  2002
• 27aWE-3 Fluctuations of correlation dimensions at the Anderson transition

  Obuse H, Yakubo K  Meeting Abstracts of the Physical Society of Japan  57-  (0)  650  -650  2002  [Not refereed][Not invited]
  
• Universality of Exponents in a Two-Dimensional Delocalization Transition

  Yakubo K.  Meeting Abstracts of the Physical Society of Japan  56-  (2)  519  -519  2001
• ac current in a driven mesoscopic ring

  Ohe J., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  56-  (1)  593  -593  2001
• Transfer-Matrix Approach to Two-Dimensional Electron Transport in Inhomogeneous Magnetic Fields

  Yakubo K.  Meeting Abstracts of the Physical Society of Japan  56-  (1)  639  -639  2001
• Quantum effects on the ac conductivity in a 2D ramdom magnetic field

  Shima H., Yakubo K., Nakayama T.  Meeting abstracts of the Physical Society of Japan  55-  (2)  565  -565  2000/09/10
• Quenching of photon-assisted tunneling

  Ohe J., Yakubo K.  Meeting Abstracts of the Physical Society of Japan  55-  (2)  576  -576  2000
• Photon-Assisted Tunneling in a Driven Mesoscopic Ring

  Yakubo K., Yamaguchi A., Ohe J.  Meeting Abstracts of the Physical Society of Japan  55-  (2)  577  -577  2000
• 26aD-5 Coherent transport through a driven two-terminal interferometer

  Ohe Jun-ichiro, Yakubo Kousuke  Meeting abstracts of the Physical Society of Japan  54-  (2)  609  -609  1999/09/03
• 24pT-9 Nonequilibrium ac current in dynamical mesoscopic systems

  Yakubo Kousuke, Ohe Jun-ichiro  Meeting Abstracts of the Physical Society of Japan  54-  (2)  203  -203  1999
• 29a-ZB-7 AB oscillation in a two-terminal electronic interferometer with a time-varying

  Yakubo Kousuke, Ohe Jun-ichiro  Meeting Abstracts of the Physical Society of Japan  54-  (1)  588  -588  1999
• Dynamics of random presence of solid/liquid phases. (Ministry of Education S)

  中山恒義, 矢久保考介, 寺尾貴道  複雑液体における協力現象 平成9年度 ミクロからメゾへの系統的アプローチ  1998
• Photon-assisted quantum transport in a double path interferometer

  YAKUBO Kousuke, OHE Junichiro  Meeting Abstracts of the Physical Society of Japan  53-  (2)  154  -154  1998
• Delocalization transition of a two-dimensional electron system in a random magnetic field with non-zero mean

  HIRASAKI Yasuyuki, YAKUBO Kousuke  Meeting Abstracts of the Physical Society of Japan  53-  (2)  155  -155  1998
• Phase measurement and AB oscillation in a dynamical mesoscopic system

  OHE Junichiro, YAKUBO Kousuke  Meeting Abstracts of the Physical Society of Japan  53-  (2)  162  -162  1998
• Scaling analysis of multifractal wavefunctions at the metal-insulator transition

  YAKUBO Kousuke, ONO Masaki  Meeting Abstracts of the Physical Society of Japan  53-  (1)  629  -629  1998
• 5a-E-9 Photon-assisted quantum transport in a quantum point contact

  Yakubo Kousuke, Ohe Junichiro  Meeting abstracts of the Physical Society of Japan  52-  (2)  143  -143  1997/09/16
• Dynamics of random presence system of solid phase and liquid-phase. ( The Ministry of Education, Science and Culture S ).

  中山恒義, 矢久保考介, 寺尾貴道  複雑液体における協力現象 平成8年度 ミクロからメゾへの系統的アプローチ  1997
• 29p-S-6 Two dimensional electrons in a random magnetic field

  Yakubo Kousuke  Meeting Abstracts of the Physical Society of Japan  52-  (1)  166  -166  1997
• Numerical study on photon-assisted electron transports

  Yakubo K., Tezuka T.  Meeting Abstracts of the Physical Society of Japan  1996-  (3)  453  -453  1996
• Transfer matrix technique for quantum transports in temporally oscillating external fields

  Yakubo K., Tezuka T.  Meeting Abstracts of the Physical Society of Japan  1996-  (3)  728  -728  1996
• 3a-L-11 Multifractal Analysis of 2D Electron Wavefunctions in Random Magnetic Fields

  Yakubo K., Goto Y.  Meeting Abstracts of the Physical Society of Japan  51-  (3)  669  -669  1996
• Numerical Study on Two-Dimensional Electron Systems in Random Magnetic Fields

  Goto Y., Yakubo K., Nakayama T.  Meeting Abstracts of the Physical Society of Japan  1995-  (3)  648  -648  1995
• 3p-PSA-26 Dynamical Structure Factor of Percolating Heisenberg Antiferromagnets

  TERAO T, YAKUBO K, NAKAYAMA T  Abstracts of the meeting of the Physical Society of Japan. Sectional meeting  1994-  (3)  103  -103  1994/08/16
• 4p-E-17 Vibrational Properties of Fractal Drum

  HOBIKI Y, YAKUBO K, NAKAYAMA T  Meeting Abstracts of the Physical Society of Japan  1994-  (3)  502  -502  1994
• 29p-PSB-3 Anomalous enhancement of phonon-fracton anharmonic coupling in non-linear fractal lattices

  NEMOTO M, YAKUBO K, NAKAYAMA T  Meeting Abstracts of the Physical Society of Japan  49-  (2)  269  -269  1994
• 30p-A-12 Dynamics of percolating Heisenberg antiferromagnets : Extension of the forced oscillator method

  TERAO T, YAKUBO K, NAKAYAMA T  Meeting Abstracts of the Physical Society of Japan  49-  (3)  568  -568  1994
• 強制振動子法とその応用--大規模行列の固有値解析アルゴリズム

  矢久保 考介  固体物理  28-  (8)  p527  -534  1993/08
• 13p-PSB-39 Antiferromagnetic fractons : Large scale simulations and scaling theory

  Yakubo K., Terao T., Nakayama T.  Meeting Abstracts of the Physical Society of Japan  1993-  (3)  562  -562  1993
• 13p-PSB-40 Dynamical Structure Factor of Spin-wave Fractons of Percolating Antiferromagnets

  Terao T., Yakubo K., Nakayama T.  Meeting Abstracts of the Physical Society of Japan  1993-  (3)  563  -563  1993
• 27p-PSB-29 Large-scale simulations on spin-wave fractons in two-dimensional percolating antiferromagnets

  TERAO T, YAKUBO K, NAKAYAMA T  Meeting Abstracts of the Physical Society of Japan  1992-  (3)  495  -495  1992
• 27p-PSB-30 Numerical confirmation on hyperscaling law of antiferromagnetic fracton excitations

  YAKUBO K, TERAO T, NAKAYAMA T  Meeting Abstracts of the Physical Society of Japan  1992-  (3)  495  -495  1992
• 27a-E-5 Dynamical Structure factor of Fractal Nets: Numerical study on Dynamic Scaling properties

  YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  47-  (2)  222  -222  1992
• 28a-T-11 Photon Localization in Optical Waveguides

  NAKAYAMA T, YAKUBO K, TAKANO M  Meeting Abstracts of the Physical Society of Japan  47-  (2)  382  -382  1992
• 24a-W-16 Dynamic Structure Factor of Fractal Nets : Direct Observations by Supercomputer

  YAKUBO K., NAKAYAMA T.  春の分科会講演予稿集  1991-  (2)  198  -198  1991/03/11
• 28a-A-6 Dynamic Structure Factor of Fractal Nets:Direct Obsevations by Supercomputer

  YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  46-  (2)  223  -223  1991
• 28p-R-8 A Numerical Approach to Photon Localization

  TAKANO M., YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  46-  (2)  367  -367  1991
• 30a-T-2 Localization exponent of quantum-percolation systems : Numerical study for β-function

  TERAO T., YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  46-  (3)  494  -494  1991
• Dynamical Structure Factor of Percolating Networks

  中山 恒義, 矢久保 考介, 大田 啓之  統計数理 = Proceedings of the Institute of Statistical Mathematics  38-  (1)  73  -88  1990/06
• フラクタル系のダイナミクス (ランダムなフラクタル・パタ-ンの成長機構と統計(研究会報告))

  矢久保 考介, 中山 恒義  物性研究  54-  (1)  p30  -43  1990/04  

  この論文は国立情報学研究所の電子図書館事業により電子化されました。
• 浸透網とフラクトン力学

  矢久保 考介, 中山 恒義  固体物理  25-  (3)  p141  -154  1990/03
• 4a-J-3 Eigenmodes for huge matrices : The mode separation and its judgement

  YAKUBO K., MARIS H.J., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  1990-  (4)  85  -85  1990
• 3p-P-4 Missing-modes in fractom density of states

  YAKUBO K., COURTENS E, NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  1990-  (3)  443  -443  1990
• Dynamical Structure Factor of Percolating Nets : Direct Observation by Supercomputer

  OHTA H., YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  45-  (3)  385  -385  1990
• Fracton Dynamics : New Development by Supercomputers

  Yakubo Kousuke, Nakayama Tsuneyoshi  日本物理学会誌  44-  (11)  p833  -836  1989/11
• 6p-R-1 Origin of the Hump in the DOS of Percolating Nets

  NAKAYAMA T., YAKUBO K., OHI A.  Meeting Abstracts of the Physical Society of Japan  1989-  (3)  475  -475  1989
• 6p-R-2 Vector Fractons : Its Density of States and Universarity Class

  YAKUBO K., NAKAYAMA T.  Meeting Abstracts of the Physical Society of Japan  1989-  (3)  476  -476  1989
• フラクタル系のダイナミクス

  矢久保 考介, 中山 恒義  統計数理  37-  (1)  p47  -61  1989
• 5a-C5-1 巨大パーコレーション系におけるフラクトン状態密度

  高杉 恒一, 矢久保 考介, 中山 恒義  秋の分科会予稿集  1988-  (3)  408  -408  1988
• 5a-C5-2 巨大パーコレーション・システムにおけるフラクトン超局在の実証

  矢久保 考介, 中山 恒義  秋の分科会予稿集  1988-  (3)  409  -409  1988
• Vibrational Spectra of Percolation Clusters : Alexander-Orbach Conjecture

  Yakubo Kousuke, Takasugi Kouichi, Tanaka Satoshi, Nakayama Tsuneyoshi  Bulletin of the Faculty of Engineering,Hokkaido University  (137)  p83  -92  1987/10
• Kapitza resistance between sintered metal particles and 3he舑4he mixture

  Nakayama, Tsuneyoshi, Yakubo, Kousuke  Japanese Journal of Applied Physics  26-  (S3-1)  1987
• 27p-W-1 巨大パーコレーション・クラスターのフラクトン状態密度 : Alexander-Orbachの予測

  矢久保 考介, 中山 恒義  秋の分科会予稿集  1987-  (3)  331  -331  1987
• Metal Particles : Quantum-Size Effects, Randomness and Dynamic Properties

  Yakubo Kousuke, Nakayama Tsuneyoshi  Bulletin of the Faculty of Engineering,Hokkaido University  (130)  p55  -62  1986/03
• 27p-C-4 金属微粒子による高周波フォノンの吸収と励起

  矢久保 考介, 中山 恒義  秋の分科会予稿集  1986-  (2)  418  -418  1986
• 28a-QD-9 多孔媒質と^3He-^4He混合液間のカピッツァ抵抗

  矢久保 考介, 中山 恒義  秋の分科会予稿集  1986-  (3)  265  -265  1986

Research Grants & Projects

• Mechanisms of fractality in complex networks

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2022/04 -2025/03 

  Author : 矢久保 考介, 小布施 秀明
• Fractality and long-range degree correlation in complex networks

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2019/04 -2022/03 

  Author : Yakubo Kousuke

   

  Many complex networks exhibit fractality in a topological sense. It is well known that the mechanism of this property is closely related to self-organized criticality. In this study, however, another mechanism of fractality in networks is explored by clarifying the relationship between fractality and the correlation between the number of neighboring nodes of each node (degree). Specifically, we propose mathematical models of fractal complex networks based on self-organized critical dynamics and reveal how fractality is generated from the long-range degree correlation by elucidating the relationship between fractality and the empirical fact that high degree nodes (hubs) are far away from each other.
• Origin of fractality in complex networks and self-organized criticality

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 2016/04 -2019/03 

  Author : Yakubo Kousuke

   

  Studying the origin of fractality found in many real-world complex networks, we have obtained the following results. (1) We proposed a model of fractal complex networks based on an SOC dynamics driven by the antagonistic relationship between the growth of a functional network and its cascading overload failure, (2) we have shown a fractal and small-world structures, and their structural crossover in the process of time development of the SOC model, (3) to clarify the role of a long-range repulsive correlation between hub nodes to the fractal property, long-range degree correlations in a complex network have been formulated in a quite general manner, and (4) we have elucidated that fractality cannot be realized only by nearest-neighbor degree correlations but a long-range hub repulsion is closely related to the origin of fractality.
• Basic reseach for designing functional fractal objects: Structure control and dynamics

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 2013/04 -2016/03 

  Author : Yakubo Kousuke, OBUSE Hideaki

   

  Studying various fractal systems to understand structure formation mechanisms and dynamics in a unified manner, we have obtained the following results. (1) Based on the fact that an order parameter at criticality is distributed with the generalized Gumbel distribution function, the distribution of the fractal dimension characterizing spatial profile of the local order parameter near the critical point generally obeys a triple exponential function, (2) the distribution of the fractal dimension of coastline formed by a self-organized critical (SOC) dynamics obeys the triple exponential function, (3) scale-free networks are robust against cascading failures by temporally fluctuating loads, (4) an SOC model to explain the spontaneous formation of fractal complex networks has been constructed.
• Fractal formation mechanism in hierarchically complex systems and fractal design

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 2010 -2012 

  Author : YAKUBO Kousuke, SHIMA Hiroyuki

   

  In this project, we have studied theoretically the fractality appearing in several hierarchical levels of complex systems. This study involves (1) clarifying universal properties in structural fluctuations and their origins, (2) understanding formation mechanisms of fractals, and (3) designing theoretically functional fractal structures. In particular, statistical properties of fractal systems in different scales, from macroscopic classical systems to nanoscale quantum ones and complex networks with no Euclidean distance, have been systematically studied.
• Study on the formation process of fractal structures with large-scale hierarchal systems

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

  Date (from‐to) : 2007 -2009 

  Author : NAKAYAMA Tsuneyoshi, YAKUBO Kousuke, SHIMA Hiroyuki

   

  The results are summarized as follows : 1) We have provided the theoretical basis, according to fluid mechanics, on the relationship between fractal dimensions of aggregates and sedimentation velocity. 2) We have theoretically presented the probability distribution function of the fractal dimension characterizing critical fractal systems. 3) We have demonstrated that there holds the dynamic scaling law in inelastic neutron scattering data for anti-ferromagnetic percolating systems. 4) We have clarified the relation between the fractal and the small-world properties of complex network systems.
• Theoretical approach to zero-bias transport by quantum pumping and its applications

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 2007 -2009 

  Author : YAKUBO Kousuke, NAKAYAMA Tsuneyoshi, SHIMA Hiroyuki

   

  In this project, we have clarified theoretically several properties of zero-bias currents induced by a quantum pumping mechanism by utilizing a novel transfer matrix approach developed by us. In particular, we found that non-adiabatic quantum pumping in a rather simple system can realizes large magnitudes of charge currents or pure spin currents without accompanying any charge currents.
• 光駆動型分子ローターを利用した新機能分子システムの開発

  日本学術振興会：科学研究費助成事業 萌芽研究

  Date (from‐to) : 2006 -2007 

  Author : 中山 恒義, 矢久保 考介, 島 弘幸

   

  超短光パルスを利用した分子ナノ操作・測定技術は、フェムト秒分光・光ピンセットなどの技術開発を受け、近年着実な進歩を遂げている。しかし既存技術に基づく分子配向の制御可能範囲は、静止した単一分子の操作に留まっており、分子集団の動的な振る舞いを制御する技術は開発途上にある。また、回転素子の分子配向・電子状態を精密に制御するには、分子間に働く多体効果と量子揺らぎの両者を考慮した新たな制御理論の構築が不可欠である。このような課題を克服するため本申請課題では、光子場中の分子が示す量子的回転運動の特殊な対称性に着目し、回転運動に関与する量子状態を選択的に励起する分子配向制御機構をデザインした。これと並行して、大規模数値シミュレーションに基づく本制御理論の最適化を行った。その結果、分子の振動・回転時間スケールより短い時間幅を持つ超短光パルスを用いることで、分子に瞬間的な撃力を分子に与え、分子回転に関連する量子状態のみを選択的に励起することが可能であることを理論的に明らかにした。さらに、光パルスの位相と分子の量子状態が示す対称性をうまく整合させることで、分子配向と量子状態の動的制御が可能となることがわかった。これらの結果は、極性分子間に働く双極子相互作用効果を利用することで、多数の分子集団に対する高効率なコヒーレント配向制御が実現できることを示唆するものであり、位相制御光を利用した量子回転子の制御技術として意義の高い成果である。
• Formation of fractal structures and the development of its simulation algorithms

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

  Date (from‐to) : 2004 -2006 

  Author : NAKAYAMA Tsuneyoshi, YAKUBO Kousuke, SHIMA Hiroyuki

   

  The research on the formation of fractal patterns attracts much attention of physicists according to its universality and generality. To reveal the physical origin of the formation of fractal patterns, it has not been successful in terms of convertional approaches such as computer simulations. There has been numerous unsolved problems for this subject. The goal of the present research is to reveal the the physical origin of fractal pattern formation by means of employing quite new numerical techniques. Our goal is (1) to handle freely 10^7×10^7 matrices and (2) to apply our numerical algorithm to quantum and classical fractal structures. Our method is unique, different from other conventional methods, to map the eigenvalue problem to the problem of lattice vibrations. By applying this method, we have succeeded to obtain new results for our subject.
• 傾斜格子系における特異な励起状態に関する研究

  Date (from‐to) : 2006
• 量子回転子機能デバイスの提唱と創製

  日本学術振興会：科学研究費助成事業 萌芽研究

  Date (from‐to) : 2004 -2005 

  Author : 中山 恒義, 矢久保 考介, 島 弘幸

   

  本年度の主な成果二点を以下に述べる。 (1)多体回転子系デバイスの開発研究:本研究の主な目的は、ナノスケールで回転運動する双極子分子の分子配向を利用した新規な量子回転子デバイスを、開発・デザインすることにある。最終年度は、双極子モーメントを有する表面吸着分子を取り上げ、複数の分子間に働く双極子相互作用が系のナノ力学に与える影響を定量的に調べた。その結果、回転子間の相互作用は、誘電応答関数の非線形性を生むことが明らかとなった。さらには、極性不純物を含む物質一般に拡張し、それら一連の物質の誘電異常が我々の提唱するデバイスモデルを用いて統一的に解釈できることを示した。 (2)多体回転素子の光制御:超短パルス光を用いて量子回転子の分極配向を制御する技術は、ナノマニピュレーション技術の一環として非常に価値の高い問題である。そこで最終年度では、光パルス照射下の量子回転子のダイナミクスに関する実時間・実空間シミュレーションを行い、パルス方向への回転子の誘電分極と回転子間の相互作用との関係を昨年度に続き調べた。その結果、分極モーメントの配向が、光パルスや偏極磁場により完全に制御できることを実証し、論文発表した。さらに、これと同様の現象が、分子膜中の量子回転子についても観測される可能性を別の論文として発表した。
• 複雑ネットワークの統計的性質

  基礎科学研究

  Date (from‐to) : 2005
• Statistical Properties of Complex Networks

  Basic Science Research Program

  Date (from‐to) : 2005
• Theoretical Study of Two Dimensional Electronic States in Random Magnetic Fields and Their Transport

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 2002 -2004 

  Author : YAKUBO Kousuke, NAKAYAMA Tsuneyoshi, SHIMA Hiroyuki

   

  The aim of this research is to clarify quantum states of two-dimensional electrons in a random magnetic field and their transport properties by using various numerical techniques which we have developed so far, such as the forced oscillator method, the finite-size multifractal analysis, and the transfer matrix technique in in homogeneous magnetic fields. To this end, we have mainly studied transport properties of two-dimensional electrons in continuous systems subject to random magnetic fields with long range correlations in this year. For realizing a two-dimensional electron system in a random magnetic field experimentally, a possible method is to configure randomly ferromagnetic small particles near the surface of the two-dimensional electron system. In order to study theoretically quantum transport of such a system, we have calculated conductance of a system subject to an in homogeneous magnetic field made by a single magnetic particle by the recursive Green's function method. For this magnetic field, we have a closed line on the electron surface at which B_z=0. Electrons meander around this line (snake orbit). We can expect the Aharonov-Borm effect due to magnetic fluxes threading this loop. The conductance calculated by the recursive Green's function method shows this type of effects. Considering electron spins, the effect of the Berry phase due to a magnetic field rotating adiabatically around the electron has been found. Furthermore, we discovered that the period of Aharonov-Borm oscillation becomes shortened as increasing the strength of the magnetic field. This is because the incident energy of the electron is shifted by the Zeeman energy depending on the electron spin. In this study, we also examined statistical properties of anomalously localized states at the critical point to clarify the effect of fluctuations of random magnetic fields. In particular, we performed preliminary calculations for two-dimensional critical wave functions belonging to the symplectic class. As a result, we found that anomalously localized states at the critical point exist even in infinite systems with a finite probability. This implies that a scaling theory or renormalization group theory can be applied only to typical states.
• New Numerical Method for Analysis of Large Matrices

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

  Date (from‐to) : 2001 -2003 

  Author : NAKAYA Tsuneyoshi, SHIMA Hiroyuki, YAKUBO Kousuke

   

  The aim of this research project is to develop the efficient algorithm for the eigenvalue analysis of very large matrices of [10^6×10^6], and computing dynamic correlation functions of the systems described by those matrices. In addition, we try to extend this numerical to apply for method non-Hermitian large-scale matrices. In these term, we have succeeded to develop the algorithm to use any type of large-scale matrices. We have also applied this algorithm to actual physical systems and demonstrated its surprising efficiency.
• 臨界系の揺らぎに関する理論的研究

  Date (from‐to) : 2002
• Development of Fast Algorithm for Dynamic Correlation Functions

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 1998 -2000 

  Author : NAKAYAMA Tsuneyoshi, YAKUBO Kousuke

   

  The aim of this research project is to develop the algorithm efficient for the eigenvalue analysis and computing dynamic correlation functions. In addition, we extend this algorithm to the Hermitian and non-Hermitian large-scale matrices. In this fisical year, we have succeeded to extend the algorithm as applicable any type of large-scale matrices. We have also applied this algorithm to various physical systems and demonstrated its efficiency.
• Theoretical Study of Two-Dimensional Electronic States in a Random Magnetic Field

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

  Date (from‐to) : 1998 -1999 

  Author : YAKUBO Kousuke, NAKATYAMA Tsuneyoshi,Kousuke

   

  In recent years there has been a growing interest in two-dimensional electrons in a random magnetic field. Instead of importance of the problem, there still exist many unsolved questions in this field. We have studies the localization property of two-dimensional electrons in random magnetic fields in terms of a novel finite-size scaling based on the multifractality of the critical wave function. At first, we have determined the existence of the metal-insulator transition in a system subject to a random magnetic field with vanishing mean and its universality class. The result suggests that all electronic states are localized in such systems. We also investigated systems in a random magnetic field with finite mean. In the case that the average field is much stronger than the magnitude of field fluctuations, the spectrum separates into Landau subbands and only the states at subband centers are extended as predicted by a semiclassical theory. We confirmed that the universality class of this transition is the same with that of the integer quantum Hall system. Furthermore, the energy of the extended state shifts upward from the subband center when the magnitude of field fluctuation becomes stronger. These results are quite important for understanding electron transport in a fractional quantum Hall system near v=1/2.
• 固相-液相ランダム共存系の動力学

  日本学術振興会：科学研究費助成事業 重点領域研究

  Date (from‐to) : 1997 -1997 

  Author : 中山 恒義, 寺尾 貴道, 矢久保 考介

   

  ガラスは、約10K以下でのTに比例する比熱、10K領域での熱伝導率のプラトー、そしてラマン散乱における50cm^<-1>前後での幅の広いピークいわゆるボゾン・ピークの存在などミクロな構造によらない普遍的な諸性質を示すことでよく知られている。Tに比例する比熱に関しては、原子集団のトンネリング・モデルに基づく広いエネルギー分布を有する二準位系の存在の「仮定」により説明される。また熱伝導率の10K近くでのプラトーに関しては、何らかの原因で音響フォノンが強く局在していることが関与していると考えられている。しかしながら、強い局在状態が導かれる構造的な意味での起源は明らかにされていなかった。これが明らかになればガラスの動的性質、すなわち極低温から高温または低エネルギーから高エネルギー領域までの、普遍的かつ特異なガラスの性質の解明につながるものと考えられている。最近、a-SiO_2に対して高分解能非弾性X散乱実権(SOR)が、グルノ-ブルで相次いで行われた。すなわちコヒーレント非弾性中性子散乱実権ではカバーできない低エネルギー領域でのS(q.ω)の知見が得られるようになった。これによると一つはボゾン・ピークを観測し、もう一つの実験では分散性すなわちq依存性を持つ音響モードの存在が示唆されている。本年度の研究では、ガラスの本質的な構造だけを取り入れた単純化されたモデルで、ガラスに関する普遍的な動的諸性質がよく説明されることを示した。 また本年度の研究では、水に対する簡単化された構造モデルを用いて、動的構造因子S(q.ω)を計算し、上記の非弾性X線散乱実験で得られたS(q,ω)の振る舞いと比較することにより、その物理的起源を明らかにした。これらの結果を踏まえラマン散乱分光に現れる幅の広い60cm^<-1>と180cm^<-1>のピークは、質的に異なった局在モードが関与していることを明らかにした。
• PAT過程における電子位相変化とPATデバイス構造の最適化に関する理論的研究

  日本学術振興会：科学研究費助成事業 重点領域研究

  Date (from‐to) : 1997 -1997 

  Author : 矢久保 考介

   

  本研究では、新しい転送行列法を用いることによって、Photon Assisted Tunneling(PAT)による大きな電流変化が起こる系を理論的にデザインし、I-V特性や光照射抵抗などを定量的に計算した。単一障壁系や二重障壁系において有効な光照射効果が得られないことは、以前の我々の研究によって明らかにされている。その研究によると、系に共鳴トンネル準位が存在し、かつその準位を通る電子の透過率が小さい場合に大きな光照射効果が得られることになる。この知見をもとに、本研究では非対称三重障壁系におけるPAT効果について数値的な研究を行なった。その結果、非対称三重障壁系でのPAT効果は、二重障壁系のそれに比べ100倍以上も大きいことが明らかになった。本研究ではさらに、PAT効果によるコンダクタンスの温度依存性、および光強度依存性についても数値的研究を行なった。本研究の数値計算に用いられたアルゴリズムは、通常の転送行列法をエネルギーが保存しない系に対しても使えるように拡張したもので、シュレ-ディンガー方程式の直接積分に比べて10^4倍も高速に計算できる。この方法を用いることによって、本研究で対象としたような三重障壁を持つ複雑な系を数値的に研究することが可能となった。
• 非線形カントール超格子における局在励起崩壊に関する数理的研究

  日本学術振興会：科学研究費助成事業

  Date (from‐to) : 1996 -1996 

  Author : 矢久保 孝介

   

  非線形カントール超格子構造および非線形フラクタル格子、フラクタル・ドラムのダイナミクスを動的スケーリング理論とスーパーコンピュータを用いた大規模シミュレーションにより調べ、カントール超格子、フラクタル格子およびフラクタル・ドラム上の局在振動が非線形性によってどのような影響を受けるのかを明らかにした。具体的には、力学的性質の異なる二種類の媒質をカントール集合と同じ規則性に従って並べた超格子モデルを考え、この上に励起される強局在振動モード「フラクトン」の寿命、非調和拡散、有効非線形強度等を計算した。また、フラクタル格子としては、非線形ボンド・パーコレーション系を、フラクタル・ドラムとしてはコッホ曲線をその周縁曲線とするコッホ・ドラムを用いた。数値計算では、10^6以上の自由度を有する離散カントール系およびコッホドラムの非線形振動を強制振動子法という以前我々が開発したアルゴリズムを用いて計算し、特定の線形局在振動からのエネルギー散逸の時間・空間依存性を求めることにより、非線形性によるフラクトン・モードの不安定性を解析した。非線形フラクタル格子上の強局在振動励起は非常に大きな有効非線形結合を持つことが実験的に示されているが、本研究による数値計算結果でも強局在振動モードの非調和崩壊寿命は、通常の拡がったモードに比べて極めて長くなることが示された。
• 固相-液相ランダム共存系の動力学

  日本学術振興会：科学研究費助成事業 重点領域研究

  Date (from‐to) : 1996 -1996 

  Author : 中山 恒義, 寺尾 貴道, 矢久保 考介

   

  トポロジカルに乱れた弾性体が粘性液体中に侵されている物理系は、自然界にその例を多く見ることができる。クラスターやドロップレットが形成されている液体、液層から固相への相転移やゾル-ゲル転移点におけるゾルとゲルの共存系などはそのような系の典型と考えられる。 本研究では3次元のグラスター・クラスター凝集モデルにおける動的性質、特にその振動励起に関する振る舞いについて明らかにすることを目的とする。特に振動状態密度並びに動的構造因子における振動数依存性について明らかにする。クラスター・クラスター凝集モデルに基づき、系のサイズが大きな凝集体を様々な粒子濃度に関して、コンピュータ・シミュレーションにより計算した。3次元立法格子上において、系の境界条件はすべての方向に関して周期境界とした。系が自己相似性を有するならば、密度相関関数g(r)≡〈p (r′) p (r+r′) 〉はrに関してベキ的な性質を示す。すなわち系のg(r)を計算することによりフラクタル次元D_rを求めることができる。その結果、いずれもある特徴的な長さスケールよξり短いところできれいなベキを示すことが分かった。 次に、得られた系の振動状態密度を並列計算に適したアルゴリズムである強制振動子法により求め、その振動数依存性および系の濃度既存性について明らかにした。得られたベキ依存性の指数等に関して、従来行われている実験結果と比較した。これからスペクトル次元はd_f=1.17±0.04と求められる。これはシリカ・エアロゲルに関して行われている実験結果とよく一致している。また、クラスター・クラスター凝集モデルにおける動的構造因子を強制振動子法により数値的に求めた。計算された動的構造因子の振動依存性に関する解析を行い、そのスケーリング性質について明らかにした。
• 固相-液相ランダム共存系の動力学

  日本学術振興会：科学研究費助成事業 重点領域研究

  Date (from‐to) : 1995 -1995 

  Author : 中山 恒義, 矢久保 考介

   

  本研究では、ランダム・フラクタル構造上のフラクトン振動が、周りの粘性媒質によってどのように減衰していくか、またその減衰は系の臨界性や振動数とどのような関係があるかについて、スーパー・コンピュータを駆使した大規模計算機シミュレーションにより明らかにする事を目的とする。具体的には、2次元及び3次元の線形弾性浸透網が層流流体としての粘性媒質としての侵されている系を考えた。フラクトン励起の特徴から、強いエネルギー減衰を起こす部分は、系全体に比べて極めて狭い空間的領域となる。 我々は、このような予想を以前我々が開発したアルゴリズム出ある強制振動子法とスーパー・コンピュータを利用した大規模シミュレーションにより実証すると共に、これらの異常減衰の効果が臨界現象に果たす役割についても解明した。平成7年度には、上記モデルの最も単純な場合、すなわち2次元浸透網上のスカラー変位振動を考えて、系に起こる物理現象の本質を探った。フラクトン・モードの振動数を増大させると、その局在長はベキ的に減少するが、振幅分布の不連続性の程度は増大した。これら2つの要因は、Q値の大きさに対して正反対の効果を生じさせた。我々はフラクトン・モードのQ値が振動数に対してどのように依存するかを数値計算により調べた。
• Light Localization and Nonlinearity in Aperiodic Waveguids

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for General Scientific Research (C)

  Date (from‐to) : 1994 -1995 

  Author : NAKAYAMA Tsuneyoshi, YAKUBO Kousuke

   

  The purpose of this project is to investigate the strong localization of light waves in aperiodic waveguides. In particular, we have payd attention to a role of nonlinearity to the localization of light. Followings were clarified, (i) it became clear that the strong localization of light surely occurs (ii) the nonlinearity enhances the localization. Those results were obtained via largescale computer simulations.
• Development of Algorithm for Eigenvalue Analysis of Very Large Matrices

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research Grant-in-Aid for Developmental Scientific Research (B)

  Date (from‐to) : 1993 -1995 

  Author : NAKAYAMA Tsuneyoshi, KAKUMA Seiichi, MIZUNO Seiji, TAKANO Motohiro, YAKUBO Kousuke

   

  This research project aims to develope the powerful algorithm suitable for very large matrices of the order of 10^7. The method is based on the mapping of the eigenvalue problem to lattice dynamics. The method is unique, compared with the other well known methods like the Lanezos method. Namely, the time-consuming part is mainly used for solving the time-development equation of motion. The efficiency was demonstrated by applying fractal systems and the mode analysis of sophistcated waveguides.
• フォトンの強い局在:大規模シミュレーションによるモデリングと可視化

  日本学術振興会：科学研究費助成事業 奨励研究(A)

  Date (from‐to) : 1993 -1993 

  Author : 矢久保 考介

   

  本研究ではまず第一に、非線形性を有しない理想的な2種類の誘電媒質をランダムに積層した系の光モード解析を行った(2種類の媒質の屈折率は現実の物質を想定して設定された)。はじめにフォトンのスペクトル密度分布を我々が開発した強制振動子法により計算し、誘電媒質の超格子構造に起因したフォトニック・バンドギャップがランダムネスによりどの様に壊されていくかを調べた。次にこの様にしてできたギャップ内準位に属する光のモード・パターンを強制振動子法によって計算した。その結果、積層方向(z-方向)に対して光の強局在が起こりうることを明らかにした。また、局在長などの局在特性とフォトニック・ギャップの関係を明確にし、強局在状態を得るための基本的な条件を明らかにした。また、x,y-方向に対しても光を閉じ込めるために、上述のランダム超格子を第三の誘電媒質(クラッディング)で取り囲むことによって作られる系を考えた。クラッディングは、光の回り込みを許す働きをするため、z-方向に対する光局在を弱める効果を持つと考えられるが、計算の結果この様な系においてもなお光の強局在が維持されることを明らかとなった。さらに本研究では、光導波路に非線形性を導入し、モデルをより現実的なものにし、実験的に光の強局在状態が観測される可能性について議論した。計算の結果、媒質の非線形性は局在光モードの自己収束現象を引き起こし、局在をさらに強める効果があることが明かとなった。
• Dynamics of Fractal Structures

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 1991 -1992 

  Author : NAKAYAMA Tsuneyoshi, OTSUKI Toshiya, MATSUSITA Mitsugu, YAKUBO Kousuke, PIMENTAL Iveta, ALEXANDER Shlomo, BRUINSMA Robin, ORBACH Raymond

   

  There are a number of physical systems exhibiting measurable dynamical properties which exhibit fractal geometry. Examples are : site-diluted magnetic structures, silica aerogels and glasses and amorphous materials. Computer simulations are essential to develop the insight into the dynamics of fractal structures, i.e., they do more than simply verify physical assumptions. The purpose of this project is to understand the very nature of the excitations of strongly random structures, and ultimately enable the investigator to develop phenomenological expressions for physical quantities. This project will shed considerable light on the debate over the use of scaling for the interpretation of light scattering experiments, as well as for the calculation of matrix elements for vibrational (hopping) transport processes.
• Dynamical properties of large-scale fractal networks

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 1990 -1991 

  Author : NAKAYAMA Tsuneyoshi, YAKUBO Kousuke

   

  Computer simulations are essential to develop the insight into dynamics of percolating nets. We have succeeded in treating very large percolation clusters of more than 10^5 particles, revealing a wealth of detailed quantitative information. These have become possible with the advent of array-processing supercomputers, and with the use of a numerical method that does not require diagonalization. The vibrational densities of states for these large percolating networks obtained. It was confirmed for both 2d- and 3d-networks, that the vibrational denisity of states is proportional to w^df with d_f close to 4/3 in the regime above the characteristic frequency w_c. We also found that fracton modes possess a quite unique character, i. e., the core of fracton excitations falls off sharply at their edges. This is in contrast with the case of homogeneously extended modes (phonons), in which the change in their amplitudes is correlated smoothly over a long distance.
• フラクタル系の動力学:フラクトン励起の超局在機構とホッピング伝導

  日本学術振興会：科学研究費助成事業

  Date (from‐to) : 1989 -1989 

  Author : 矢久保 考介
• ランダム磁場中の電子局在とそのユニバーサリティ・クラス
• Localized electrons in a random magnetic field and its universality class

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Position History

• 2016年4月1日 

  - 

  2017年3月31日 

  教育改革室室員
• 2017年4月1日 

  - 

  2019年3月31日 

  大学院工学院副学院長
• 2017年4月1日 

  - 

  2019年3月31日 

  大学院工学研究院副研究院長