Kita Takafumi

Faculty of Science　Physics　Electronic Condensed Matter PhysicsProfessor
Last Updated :2025/01/15

■Researcher basic information

Degree

  • 03/1988: Ph.D (University of Tokyo), The University of Tokyo

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J-Global ID

Research Keyword

  • ド・ハース-ファン・アルフェン効果
  • 第二種超伝導体
  • エントロピー
  • ボーズ・アインシュタイン凝縮
  • 量子渦
  • 渦糸の動力学
  • グリーン関数
  • 上部臨界磁場
  • 超流動3He
  • アルカリ原子気体
  • 自発的対称性の破れ
  • 場の量子論
  • 超流動^3He
  • ボゴリュボフ励起
  • 超低温
  • 渦糸格子状態
  • 時間反転対称性の破れ
  • 量子輸送方程式
  • ^3Heの軌道角運動量
  • 異方的超伝導
  • スピン磁化率
  • ゲージ不変性とホール効果
  • 電気抵抗
  • 輸送方程式
  • 準粒子状態
  • 超伝導の理論
  • 真木パラメータ
  • 非平衡統計力学
  • 超流動
  • 超伝導
  • Nonequilibrium Statistical Mechanics
  • Theoretical Condensed Matter Physics

Research Field

  • Natural sciences, Magnetism, superconductivity, and strongly correlated systems

■Career

Career

  • Aug. 2020 - Present
    北海道大学大学院理学研究院, 教授
  • 2010 - Jul. 2020
    北海道大学 大学院理学研究院, 准教授
  • 1995
    - 同大学助教授（大学院理学研究科物理学専攻) 助教授
  • 1995
    - Associate Professor
  • 1993
    - 北海道大学助教授（理学部物理学科数理物理学第一） 助教授
  • 1993
    - Associate Professor
  • 1993
    05/1993: Associate Professor, Department of Physics, Hokkaido University
  • 1988
    - 東京大学助手（物性研究所理論部門） 助手
  • 1988
    - Research Associate
  • 1988
    04/1988: Research Associate, Institute for Solid-State Physics, University of Tokyo
  • 1985
    - 東京大学助手（工学部物理工学科） 助手
  • 1985
    - Research Associate,10/1985: Research Associate, Department of Applied Physics, University of Tokyo

Educational Background

  • 1985, The University of Tokyo, 工学系研究科, 物理工学専攻博士課程中退, Japan
  • 1985, The University of Tokyo, Graduate School, Division of Engineering
  • 1984, The University of Tokyo, 工学系研究科, 物理工学専門課程, Japan
  • 1984, The University of Tokyo, Graduate School, Division of Engineering
  • 1982, The University of Tokyo, The Faculty of Engineering, Department of Applied Physics, Japan
  • 1982, The University of Tokyo, Faculty of Engineering

■Research activity information

Papers

  • How Infrared Singularities Affect Nambu-Goldstone Bosons at Finite Temperatures
    Takafumi Kita
    Journal of the Physical Society of Japan, 92, 054004, May 2023, [Peer-reviewed], [Lead author, Last author, Corresponding author]
    English, Scientific journal, 33948372
  • Legendre Transformation of the Luttinger–Ward Functional from the Bare Interaction Vertex to the Renormalized One
    Takafumi Kita
    Journal of the Physical Society of Japan, 91, 11, Physical Society of Japan, 15 Nov. 2022, [Peer-reviewed], [Lead author, Corresponding author]
    Scientific journal, 33948372
  • Charging in the vortex lattice of type-II superconductors
    Marie Ohuchi, Hikaru Ueki, Takafumi Kita
    Physical Review B, 105, 6, American Physical Society (APS), 22 Feb. 2022, [Peer-reviewed], [Corresponding author]
    Scientific journal
  • Quantum Field Theory of Correlated Bose–Einstein Condensates: II. Ward–Takahashi Identities and Correlation Functions
    Takafumi Kita
    Journal of the Physical Society of Japan, 90, 2, 024002, 024002, Physical Society of Japan, 15 Feb. 2021, [Peer-reviewed], [Lead author]
    English, Scientific journal, 33948372
  • Quantum Field Theory of Correlated Bose–Einstein Condensates: I. Basic Formalism
    Takafumi Kita
    Journal of the Physical Society of Japan, 90, 2, 024001, 024001, Physical Society of Japan, 15 Feb. 2021, [Peer-reviewed], [Lead author]
    English, Scientific journal, 33948372
  • Zero-Field Surface Charge Due to the Gap Suppression in d-Wave Superconductors
    Ezekiel Sambo Joshua, Hikaru Ueki, Wataru Kohno, Takafumi Kita
    Journal of the Physical Society of Japan, 89, 10, 104702, 104702, Physical Society of Japan, Oct. 2020, [Peer-reviewed], [Corresponding author]
    Scientific journal
  • Drastic enhancement of the thermal Hall angle in a d-wave superconductor
    Hikaru Ueki, Hiroki Morita, Marie Ohuchi, Takafumi Kita
    PHYSICAL REVIEW B, 101, 18, AMER PHYSICAL SOC, May 2020, [Peer-reviewed]
    English, Scientific journal, A drastic enhancement of the thermal Hall angle in d-wave superconductors was observed experimentally in a cuprate superconductor and in CeCoIn5 at low temperatures and very weak magnetic field [Phys. Rev. Lett. 86, 890 (2001); Phys. Rev. B 72, 214515 (2005)]. However, to the best of our knowledge, its microscopic calculation has not been performed yet. To study this microscopically, we derive the thermal Hall coefficient in extreme type-II superconductors with an isolated pinned vortex based on the augmented quasiclassical equations of superconductivity with the Lorentz force. Using it, we can confirm that the quasiparticle relaxation time and the thermal Hall angle are enhanced in d-wave superconductors without impurities of the resonant scattering because quasiparticles around the gap nodes which become dominant near zero temperature are restricted to the momentum in a specific orientation. This enhancement of the thermal Hall angle may also be observed in other nodal superconductors with large magnetic-penetration depth.
  • A Renormalization-Group Study of Interacting Bose–Einstein Condensates: II. Anomalous Dimension η for d<4 at Finite Temperatures
    Takafumi Kita
    Journal of the Physical Society of Japan, 88, 10, 104003, 104003, Physical Society of Japan, Oct. 2019, [Peer-reviewed], [Lead author]
    Scientific journal
  • Specific Heat of Superfluid 4He: Why Does It Deviate from the T3 Law at Low Temperatures?
    Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 88, 8, PHYSICAL SOC JAPAN, Aug. 2019, [Peer-reviewed], [Lead author]
    English, Scientific journal, The specific heat of superfluid He-4 measured with high precision by Greywall [Phys. Rev. B 18, 2127 (1978)] exhibits downward deviations from the expected T-3 law below about 200 mK. The behaviors can be an intrinsic effect of manifesting long-range fluctuations with an anomalous dimension in the single-particle density matrix. according to our recent renormalization-group study on Bose-Einstein condensates [T. Kita, J. Phys. Soc. Jpn. 88, 054003 (2019)].
  • Variational Approach to Many-Body Problems Incorporating Many-Body Effects at Finite Temperature
    Akimitsu Kirikoshi, Wataru Kohno, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 88, 6, PHYSICAL SOC JAPAN, Jun. 2019, [Peer-reviewed]
    English, Scientific journal, We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this formalism to weakly interacting Bose-Einstein condensates to incorporate the dynamical 3/2-body processes, which are considered important in the dynamical properties. The processes lower the free energy below the mean-field Hartree-Fock-Bogoliubov's value in the same way as a previous zero-temperature formalism. From our numerical results, the pair creation or annihilation processes neglected in the Popov-Shohno approximation are enhanced, particularly in the long wavelength region, owing to the many-body effects. Because the 3/2-body correlations give a finite contribution to the self-energy of quasiparticles, they may change the microscopic properties qualitatively, even in the weak-coupling region.
  • A Renormalization- Group Study of Interacting Bose-Einstein Condensates: Absence of the Bogoliubov Mode below Four (T>0) and Three (T=0) Dimensions
    Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 88, 5, PHYSICAL SOC JAPAN, May 2019, [Peer-reviewed], [Lead author]
    English, Scientific journal, We derive exact renormalization-group equations for the n-point vertices (n = 0, 1, 2,...) of interacting single-component Bose-Einstein condensates based on the vertex expansion of the effective action. They have a desirable feature of automatically satisfying Goldstone's theorem I, which yields the Hugenholtz-Pines relation Sigma(0) - mu = Delta(0) as the lowest-order identity. Using them, it is found that the anomalous self-energy Delta(0) vanishes below d(c) = 4 (d(c) = 3) dimensions at finite temperatures (zero temperature), contrary to the Bogoliubov theory predicting a finite "sound-wave" velocity v(s) proportional to [Delta(0)](1/2) > 0. In other words, Bose-Einstein condensates are free from interactions at the excitation threshold. It is also argued that the one-particle density matrix rho(r) equivalent to <(psi) over cap (dagger)(r(1))(psi) over cap (r(1) + r)> for d < d(c) dimensions approaches the off-diagonal-long-range-order value N-0/V asymptotically as r(-d+2-eta) with an anomalous dimension eta > 0. The additional exponent. at finite temperatures is predicted to behave for d = 4 - epsilon dimensions (0 < epsilon << 1) as eta proportional to epsilon(2). Thus, the interacting Bose-Einstein condensates are subject to long-range fluctuations similar to those at the second-order transition point, and their excitations in the one-particle channel are distinct from the Nambu-Goldstone mode with a sound-wave dispersion in the two-particle channel.
  • Variational Wave Function for Inhomogeneous Bose-Einstein Condensate with 3/2-Body Correlations
    Watani Kohno, Akimitsu Kirikoshi, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87, 12, PHYSICAL SOC JAPAN, Dec. 2018, [Peer-reviewed]
    English, Scientific journal, We construct a variational wave function for inhomogeneous weakly interacting Bose-Einstein condensates beyond the mean-field approximation by incorporating 3/2-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the 3/2-body correlations give a contribution comparable to the mean-field energy toward lowering the ground-state energy.
  • Number-Phase Fluctuations in Isolated Superconductors
    Xiaotian Si, Wataru Kohno, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87, 10, PHYSICAL SOC JAPAN, Oct. 2018, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We improve the Bardeenn Cooper Schrieffer wave function with a fixed particle number so as to incorporate many-body correlations beyond the mean-field treatment. It is shown that the correlations lower the ground-state energy far more than Cooper-pair condensation in the weak-coupling region. Moreover, they naturally bring a superposition over the number of condensed particles. Thus, Cooper-pair condensation is special among the various bound-state formations of quantum mechanics in that number fluctuations are necessarily present in the condensate through the dynamical exchange of particles with the non-condensate reservoir. On the basis of this result, we propose Delta N-con . Delta phi greater than or similar to 1 as the uncertainty relation relevant to the number-phase fluctuations in superconductors and superfluids, where the number of condensed particles N-con is used instead of the total particle number N. The formula implies that a macroscopic phase phi can be established even in number-fixed superconductors and superfluids since Delta N-con >> 1.
  • Charging in a Superconducting Vortex Due to the Three Force Terms in Augmented Eilenberger Equations
    Hikaru Ueki, Marie Ohuchi, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87, 4, PHYSICAL SOC JAPAN, Apr. 2018, [Peer-reviewed]
    English, Scientific journal, We derive augmented Eilenberger equations that incorporate the following missing force terms: (i) the Lorentz force, (ii) the pair-potential gradient (PPG) force, and (iii) the pressure difference arising from the slope in the density of states (DOS). Recently, augmented Eilenberger equations with the Lorentz and PPG forces have been derived microscopically by studying the Hall and charging effects in superconductors, but the pressure due to the slope in the DOS has not yet been considered in augmented Eilenberger equations, despite phenomenological indications that it is a charging mechanism in a vortex of type-II superconductors. This newly added pressure is called "the SDOS pressure". We calculate the charging in an isolated vortex of an s-wave superconductor with a spherical Fermi surface using the augmented Eilenberger equations incorporating the Lorentz force, PPG force, and SDOS pressure. When we compare the charge densities due to the three force terms in the augmented Eilenberger equations, the vortex-core charging due to the SDOS pressure is larger than that due to the other forces near the superconducting transition temperature. Thus, when we calculate the charging in an isolated vortex of a superconductor with a finite slope in the DOS, we should consider not only the Lorentz and PPG forces but also the SDOS pressure.
  • Ground-State Wave Function with Interactions between Different Species in M-Component Miscible Bose-Einstein Condensates
    Wataru Kohno, Akimitsu Kirikoshi, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 87, 3, PHYSICAL SOC JAPAN, Mar. 2018, [Peer-reviewed]
    English, Scientific journal, We construct a variational ground-state wave function of weakly interacting M-component Bose Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops into the condensate and vice versa. Our numerical results with various masses and particle numbers show that the 3/2-body processes between different particles make finite contributions to lowering the ground-state energy, implying that many-body correlation effects between different particles are essential even in the weak-coupling regime of the Bose - Einstein condensates. We also consider the stability condition for 2-component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation U-AB(2)/UAAUBB < 1 + alpha, where U-ij is the effective contact potential between particles i and j and a is the correction, which originates from the 3/2- and 2-body processes.
  • Charging due to Pair-Potential Gradient in Vortex of Type-II Superconductors
    Marie Ohuchi, Hikaru Ueki, Takafumi Kita
    Journal of the Physical Society of Japan, 86, 7, 073702, 073702, Physical Society of Japan, 15 Jul. 2017, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, Besides the magnetic Lorentz force familiar from the Hall effect in metals and semiconductors, there exists a mechanism for charging peculiar to superconductors that is caused by the pair-potential gradient (PPG). We incorporate it in the augmented quasiclassical equations of superconductivity with the Lorentz force to study charging of an isolated vortex in an equilibrium s-wave type-II superconductor. It is found that the PPG mechanism gives rise to charging concentrated within the core whose magnitude at the core center can be 10 to 102times larger than that caused by the Lorentz force. Our detailed calculations on the spatial, temperature, and magnetic-penetration-depth dependences of the vortex-core charge reveal that the PPG mechanism contributes dominantly to the core charging of the isolated vortex over a wide parameter range. The two mechanisms are also found to work additively at the core center for the present model with an isotropic Fermi surface.
  • 3/2-Body Correlations and Coherence in Bose–Einstein Condensates
    Takafumi Kita
    Journal of the Physical Society of Japan, 86, 4, 044003, 044003, Physical Society of Japan, 15 Apr. 2017, [Peer-reviewed], [Lead author]
    English, Scientific journal
  • Hall Effect in the Vortex Lattice of d-Wave Superconductors with Anisotropic Fermi Surfaces
    Wataru Kohno, Hikaru Ueki, Takafumi Kita
    Journal of the Physical Society of Japan, 86, 2, 023702, 023702, Physical Society of Japan, 15 Feb. 2017, [Peer-reviewed]
    English, Scientific journal, On the basis of the augmented quasiclassical theory of superconductivity with the Lorentz force, we study the magnetic field dependence of the charge distribution due to the Lorentz force in a d-wave vortex lattice with anisotropic Fermi surfaces. Owing to the competition between the energy-gap and Fermi surface anisotropies, the charge profile in the vortex lattice changes dramatically with increasing magnetic field because of the overlaps of each nearest vortex-core charge. In addition, the accumulated charge in the core region may reverse its sign as a function of magnetic field. This strong field dependence of the vortex-core charge cannot be observed in the model with an isotropic Fermi surface.
  • Are Quasiparticles and Phonons Identical in Bose-Einstein Condensates?
    Kazumasa Tsutsui, Yusuke Kato, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 85, 12, PHYSICAL SOC JAPAN, Dec. 2016, [Peer-reviewed]
    English, Scientific journal, We study an interacting spinless Bose-Einstein condensate to clarify theoretically whether the spectra of its quasiparticles (one-particle excitations) and collective modes (two-particle excitations) are identical, as concluded by Gavoret and Nozieres [Ann. Phys. (N. Y.) 28, 349 (1964)]. We derive analytic expressions for their first and second moments so as to extend the Bijl-Feynman formula for the peak of the collective-mode spectrum to its width (inverse lifetime) and also to the one-particle channel. The obtained formulas indicate that the width of the collective-mode spectrum manifestly vanishes in the long-wavelength limit, whereas that of the quasiparticle spectrum apparently remains finite. We also evaluate the peaks and widths of the two spectra numerically for a model interaction potential in terms of the Jastrow wave function optimized by a variational method. It is thereby found that the width of the quasiparticle spectrum increases towards a constant as the wavenumber decreases. This marked difference in the spectral widths implies that the two spectra are distinct. In particular, the lifetime of the quasiparticles remains finite even in the long-wavelength limit.
  • Quantum Correlations of Ideal Bose and Fermi Gases in the Canonical Ensemble
    Kazumasa Tsutsui, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 85, 11, PHYSICAL SOC JAPAN, Nov. 2016, [Peer-reviewed]
    English, Scientific journal, We derive an expression for the reduced density matrices of ideal Bose and Fermi gases in the canonical ensemble, which corresponds to the Bloch-De Dominicis (or Wick's) theorem in the grand canonical ensemble for normal-ordered products of operators. Using this expression, we study one-and two-body correlations of homogeneous ideal gases with N particles. The pair distribution function g((2))(r) of fermions clearly exhibits antibunching with g((2))(0) = 0 due to the Pauli exclusion principle at all temperatures, whereas that of normal bosons shows bunching with g((2))(0) approximate to 2, corresponding to the Hanbury Brown-Twiss effect. For bosons below the Bose-Einstein condensation temperature T-0, an off-diagonal long-range order develops in the one-particle density matrix to reach g((1))(r) = 1 at T = 0, and the pair correlation starts to decrease towards g((2))(r) approximate to 1 at T = 0. The results for N -> infinity are seen to converge to those of the grand canonical ensemble obtained by assuming the average <(psi) over cap (r)> of the field operator (psi) over cap (r) below T-0. This fact justifies the introduction of the "anomalous" average <(psi) over cap (r)> not equal 0 below T-0 in the grand canonical ensemble as a mathematical means of removing unphysical particle-number fluctuations to reproduce the canonical results in the thermodynamic limit.
  • Hall Effect in the Abrikosov Lattice of Type-II Superconductors
    Wataru Kohno, Hikaru Ueki, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 85, 8, PHYSICAL SOC JAPAN, Aug. 2016, [Peer-reviewed]
    English, Scientific journal, We study vortex charging caused by the Lorentz force on supercurrent based on the augmented quasiclassical equations of superconductivity. Our numerical study on an s-wave vortex lattice in the range H-c1 < H < H-c2 reveals that each vortex core with a single flux quantum also accumulates charge due to the circulating supercurrent and has a Hall voltage across the core. The field dependence of the charge density at the core center is well described by rho(0) proportional to H(H-c2 - H) with a peak near H-c2/2 originating from competition between the increasing magnetic field and the decreasing pair potential. The peak value of the accumulated charge in a core region of radius 0.5 xi(0) is estimated to be about eta Delta(0)/(kF xi(0)) x broken vertical bar e broken vertical bar C per Delta z = 10 angstrom along the flux line at low temperatures, where eta = pi c(0)Delta(z)/broken vertical bar e broken vertical bar(2) = 1.09 x 10(18) J(-1) with e < 0 the charge of an electron, Delta(0) the energy gap at T = 0, k(F) the Fermi wave number, and xi(0) the coherence length at T = 0.
  • Vortex-Core Charging Due to the Lorentz Force in a d-Wave Superconductor
    Hikaru Ueki, Wataru Kohno, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 85, 6, PHYSICAL SOC JAPAN, Jun. 2016, [Peer-reviewed]
    English, Scientific journal, We derive augmented quasiclassical equations of superconductivity with the Lorentz force in the Matsubara formalism so that the charge redistribution due to supercurrent can be calculated quantitatively. Using it, we obtain an analytic expression for the vortex-core charge of an isolated vortex in extreme type-II materials given in terms of the London penetration depth and the equilibrium Hall coefficient. It depends strongly on the Fermi surface curvature and gap anisotropy, and may change sign even as a function of temperature due to the variation in the excitation curvature under the growing energy gap. This is also confirmed in our numerical study of high-T-c superconductors.
  • 19pBK-3 Study of the quasi-particle excitation of BEC
    TSUTSUI Kazumasa, KITA Takafumi, KATO Yusuke
    Meeting Abstracts of the Physical Society of Japan, 71, 658, 658, The Physical Society of Japan (JPS), 2016
    Japanese
  • 22aAY-12 Quasi-qlassical equation with the Lorentz force in Matsubara formalism
    Kouno W., Ueki H., Kita T.
    Meeting Abstracts of the Physical Society of Japan, 71, 1774, 1774, The Physical Society of Japan (JPS), 2016
    Japanese
  • 22aAY-11 Vortex-core charging in a d-wave superconductor with the Fermi-surface anisotropy
    Ueki H., Kouno W., Kita T.
    Meeting Abstracts of the Physical Society of Japan, 71, 1773, 1773, The Physical Society of Japan (JPS), 2016
    Japanese
  • Effective Action for Bose-Einstein Condensates
    Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 83, 6, PHYSICAL SOC JAPAN, Jun. 2014, [Peer-reviewed], [Lead author]
    English, Scientific journal, We clarify basic properties of an effective action (i.e., self-consistent perturbation expansion) for interacting Bose-Einstein condensates, where field psi itself acquires a finite thermodynamic average besides two-point Green's function (G) over cap to form an off-diagonal long-range order. It is shown that the action can be expressed concisely order by order in terms of the interaction vertex and a special combination of and (G) over cap so as to satisfy both Noether's theorem and Goldstone's theorem (I) corresponding to the first proof. The self-energy is predicted to have a one-particlereducible structure due to not equal 0 to transform the Bogoliubov mode into a bubbling mode with a substantial decay rate.
  • Lifetime of Single-Particle Excitations in a Dilute Bose-Einstein Condensate at Zero Temperature
    Kazumasa Tsutsui, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 83, 3, PHYSICAL SOC JAPAN, Mar. 2014, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We study the lifetime of single-particle excitations in a dilute homogeneous Bose-Einstein condensate at zero temperature based on a self-consistent perturbation expansion of satisfying Goldstone's theorem and conservation laws simultaneously. It is shown that every excitation for each momentum p should have a finite lifetime proportional to the inverse a(-1) of the s-wave scattering length a, instead of a(-2) for the normal state, due to a new class of Feynman diagrams for the self-energy that emerges upon condensation. We calculate the lifetime as a function of vertical bar p vertical bar approximately.
  • Ground-State Energy and Condensate Density of a Dilute Bose Gas Revisited
    Kazumasa Tsutsui, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 82, 6, PHYSICAL SOC JAPAN, Jun. 2013, [Peer-reviewed]
    English, Scientific journal, The ground-state energy per particle E/N and condensate density n(0) of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of Feynman diagrams for the self-energy, which has escaped consideration so far, is shown to add an extra constant c(ip) similar to O(1) to the expressions reported by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957) ] as E/N=(2 pi h(2) an/m)[1 + (128/15 root pi +16(ip)/5)root a(3)n] and n(0)/n= 1-(8/3 root pi+c(ip))\root a(3)n, where a, n, and m are are the s-wave scattering length, particle density, and particle mass, respectively. We present a couple of estimates for c(ip); the third-order perturbation expansion yields c(ip) = 0.412.
  • Studying Superfluid Transition of a Dilute Bose Gas by Conserving Approximations
    Kazumasa Tsutsui, Takafumi Kita
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 81, 11, PHYSICAL SOC JAPAN, Nov. 2012, [Peer-reviewed]
    English, Scientific journal, We consider the Bose-Einstein transition of homogeneous weakly interacting spin-0 particles based on the normal-state Phi-derivable approximation. Self-consistent calculations of Green's function and the chemical potential with several approximate Phi's are performed numerically as a function of temperature near T-c, which exhibit qualitatively different results. The ladder approximation apparently shows a continuous transition with the prefactor c = 2.94 for the transition-temperature shift Delta T-c/T-c(0) = can(1/3) given in terms of the scattering length a and density n. In contrast, the second-order, particle-hole, and fluctuation-exchange approximations yield a first-order transition. The fact that some standard Phi's predict a first-order transition challenges us to clarify whether or not the transition is really continuous.
  • Self-Consistent Approximations for Superconductivity beyond the Bardeen–Cooper–Schrieffer Theory
    Takafumi Kita
    Journal of the Physical Society of Japan, 80, 12, 124704, 124704, Physical Society of Japan, 15 Dec. 2011, [Peer-reviewed], [Lead author]
    Scientific journal
  • Properties of Nambu–Goldstone Bosons in a Single-Component Bose–Einstein Condensate
    Takafumi Kita
    Journal of the Physical Society of Japan, 80, 8, 084606, 084606, Physical Society of Japan, 15 Aug. 2011, [Peer-reviewed], [Lead author]
    Scientific journal
  • Exact results on the two-particle Green’s function of a Bose-Einstein condensate
    Takafumi Kita
    Physical Review B, 81, 21, American Physical Society (APS), 14 Jun. 2010, [Peer-reviewed], [Lead author]
    Scientific journal
  • Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
    T. Kita
    Progress of Theoretical Physics, 123, 4, 581, 658, Oxford University Press (OUP), 01 Apr. 2010, [Peer-reviewed], [Invited], [Lead author]
    Scientific journal
  • Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone’s theorem and conservation laws
    Takafumi Kita
    Physical Review B, 80, 21, American Physical Society (APS), 03 Dec. 2009, [Peer-reviewed], [Lead author]
    Scientific journal
  • Hall coefficient of equilibrium supercurrents flowing inside superconductors
    Takafumi Kita
    Physical Review B, 79, 2, American Physical Society (APS), 30 Jan. 2009, [Peer-reviewed], [Lead author]
    Scientific journal
  • Quantum Transport Equation for Bloch Electrons in Electromagnetic Fields
    Takafumi Kita, Hiromasa Yamashita
    Journal of the Physical Society of Japan, 77, 2, 024711, 024711, Japan Society of Applied Physics, 15 Feb. 2008, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We report a microscopic derivation of a quantum transport equation for Bloch electrons of metals based on the Dyson equation for the nonequilibrium Keldysh Green's function. Effects of the periodic lattice potential and external electromagnetic fields are taken into account from the beginning by expanding Green's function in terms of modified Wannier functions with the Peierls phase. We then introduce a Wigner representation of Green's function in terms of the crystal momentum and carry out the first-order gradient expansion of the Dyson equation. These procedures enable us to obtain a gauge-invariant quantum transport equation which can describe nonequilibrium evolutions of electrons in metals beyond the semiclassical Boltzmann equations and the linear response theory.
  • Entropy Change through Rayleigh–Bénard Convective Transition with Rigid Boundaries
    Takafumi Kita
    Journal of the Physical Society of Japan, 76, 6, 064006, 064006, Japan Society of Applied Physics, 15 Jun. 2007, [Peer-reviewed]
    Scientific journal
  • Conserving Gapless Mean-Field Theory of a Multi-Component Bose–Einstein Condensate
    Yoshiyuki Kondo, Takafumi Kita
    Journal of the Physical Society of Japan, 76, 2, 024008, 024008, Japan Society of Applied Physics, 15 Feb. 2007, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We develop a mean-field theory for Bose–Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz–Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from $T=0$ up to $T_{\text{c } }$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.
  • Principle of Maximum Entropy Applied to Rayleigh–Bénard Convection
    Takafumi Kita
    Journal of the Physical Society of Japan, 75, 12, 124005, 124005, Physical Society of Japan, 15 Dec. 2006, [Peer-reviewed], [Lead author]
    English, Scientific journal, A statistical-mechanical investigation is performed on Rayleigh–Bénard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression of entropy appropriate for the convection. This includes an alternative justification for the Oberbeck–Boussinesq approximation. We then calculate entropy change through the convective transition choosing mechanical quantities as independent variables. Above the critical Rayleigh number, the system is found to evolve from the heat-conducting uniform state towards the convective roll state with monotonic increase of entropy on the average. Thus, the principle of maximum entropy proposed for nonequilibrium steady states in a preceding paper [T. Kita: J. Phys. Soc. Jpn. 75 (2006) 114005] is indeed obeyed in this prototype example. The principle also provides a natural explanation for the enhancement of the Nusselt number in convection.
  • Uncommonly high upper critical field of the pyrochlore superconductor KOs2O6 below the enhanced paramagnetic limit
    T. Shibauchi, L. Krusin-Elbaum, Y. Kasahara, Y. Shimono, Y. Matsuda, R. D. McDonald, C. H. Mielke, S. Yonezawa, Z. Hiroi, M. Arai, T. Kita, G. Blatter, M. Sigrist
    Physical Review B, 74, 22, American Physical Society (APS), 07 Dec. 2006, [Peer-reviewed]
    Scientific journal
  • Entropy in Nonequilibrium Statistical Mechanics
    Takafumi Kita
    Journal of the Physical Society of Japan, 75, 11, 114005, 114005, Japan Society of Applied Physics, 15 Nov. 2006, [Peer-reviewed], [Lead author]
    Scientific journal
  • Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases
    Takafumi Kita
    Journal of the Physical Society of Japan, 75, 4, 044603, 044603, Physical Society of Japan, 15 Apr. 2006
    Scientific journal
  • Unusual upper critical field in the pyrochlore KOs2O6
    T. Shibauchi, L. Krusin-Elbaum, Y. Kasahara, Y. Shimono, Y. Matsuda, R. D. McDonald, C. H. Mielke, S. Yonezawa, Z. Hiroi, M. Arai, T. Kita, G. Blatter, M. Sigrist
    YAMADA CONFERENCE LX ON RESEARCH IN HIGH MAGNETIC FIELDS, 51, 295, +, IOP PUBLISHING LTD, 2006, [Peer-reviewed]
    English, International conference proceedings, We determine the temperature dependence of the upper critical field H-c2 in KOs2O6 from resistivity and magnetic measurements in high magnetic fields up to 50 T. By both techniques we find linear temperature dependence all the way below T-c and uncommonly high H-c2 (T -> 0 K) similar to 33 T. We show that this unusual H-c2 can be understood as a consequence of paramagnetic limit Hp remarkably enhanced by the broken spatial inversion symmetry proposed recently, ensuring that the pair-breaking here is executed by orbital degrees, associated with the smaller closed Fermi surfaces.
  • Theory of Interacting Bloch Electrons in a Magnetic Field
    Takafumi Kita, Masao Arai
    Journal of the Physical Society of Japan, 74, 10, 2813, 2830, Japan Society of Applied Physics, Oct. 2005, [Peer-reviewed], [Lead author]
    Scientific journal
  • Conserving Gapless Mean-Field Theory for Bose–Einstein Condensates
    Takafumi Kita
    Journal of the Physical Society of Japan, 74, 7, 1891, 1894, Japan Society of Applied Physics, Jul. 2005, [Peer-reviewed], [Lead author]
    English, Scientific journal, We formulate a conserving gapless mean-field theory for Bose–Einstein condensates on the basis of a Luttinger–Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$and $s$-wave scattering length $a$to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $\Delta T_{\text{c } }$from the ideal-gas result $T_{0}$is positive and given to the leading order by $\Delta T_{\text{c } } = 2.33an^{1/3}T_{0}$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose--Einstein condensates at finite temperatures.
  • Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors
    Koichi Watanabe, Takafumi Kita, Masao Arai
    Physical Review B, 71, 14, American Physical Society (APS), 29 Apr. 2005, [Peer-reviewed], [Corresponding author]
    Scientific journal
  • Ab initio calculations of Hc2 in type-II superconductors: Basic formalism and model calculations
    Takafumi Kita, Masao Arai
    Physical Review B, 70, 22, American Physical Society (APS), 29 Dec. 2004, [Peer-reviewed], [Lead author]
    Scientific journal
  • Ab Initio Calculations of Hc2 for Nb, NbSe2, and MgB2
    Masao Arai, Takafumi Kita
    Journal of the Physical Society of Japan, 73, 11, 2924, 2927, Physical Society of Japan, Nov. 2004, [Peer-reviewed]
    Scientific journal
  • Nonmagnetic Impurity Effects in MgB2
    Koichi Watanabe, Takafumi Kita
    Journal of the Physical Society of Japan, 73, 8, 2239, 2244, Physical Society of Japan, 15 Aug. 2004, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We study nonmagnetic impurity effects in MgB2 using the quasiclassical equations of superconductivity for a weak-coupling two-band model. Parameters in the model are fixed so as to reproduce experiments on MgB2 as closely as possible. The quasiparticle density of states and the specific heat are calculated for various values of the interband impurity scattering. The density of states changes gradually from a two-gap structure into the conventional single-gap structure as the interband scattering increases. It is found that the excitation threshold is not a monotonic function of the interband scattering. Calculated results for the specific heat are in good agreements with experiments on samples after irradiation.
  • Entropy and spin susceptibility of s-wave type-II superconductors near Hc2
    Takafumi Kita
    Physical Review B, 69, 14, 144507, 144507, American Physical Society (APS), 12 Apr. 2004, [Peer-reviewed], [Lead author]
    English, Scientific journal, A theoretical study is performed on the entropy Ss and the spin susceptibility s near the upper critical field Hc2 for s-wave type-II superconductors with arbitrary impurity concentrations. The changes of these quantities through Hc2 may be expressed as [Ss(T,B)–Ss(T,0)]/[Sn(T)–Ss(T,0)] = 1–αS(1–B/Hc2)=(B/Hc2)αS, for example, where B is the average flux density and Sn denotes entropy in the normal state. It is found that the slopes S and at T = 0 are identical, connected directly with the zero-energy density of states, and vary from 1.72 in the dirty limit to 0.5–0.6 in the clean limit. This mean-free-path dependence of αS and αx at T = 0 is quantitatively the same as that of the slope αp(T = 0) for the flux-flow resistivity studied previously. The result suggests that Ss(B) and Xs(B) near T = 0 are convex downward (upward) in the dirty (clean) limit, deviating substantially from the linear behavior B/Hc2. The specific-heat jump at Hc2 also shows fairly large mean-free-path dependence.
  • Theory of Flux-Flow Resistivity near Hc2 for s-Wave Type-II Superconductors
    Takafumi Kita
    Journal of the Physical Society of Japan, 73, 1, 21, 24, Physical Society of Japan, 15 Jan. 2004, [Peer-reviewed]
    Scientific journal
  • Calculation of k2(T) for s-wave type-II superconductors
    Takafumi Kita
    Physical Review B, 68, 18, 184503, 184503, American Physical Society (APS), 05 Nov. 2003, [Peer-reviewed], [Lead author]
    English, Scientific journal, This paper presents revised calculations for the Maki parameters k1 and k2 and the pair potential Δ(r) of s-wave type-II superconductors near the upper critical field Hc2 with arbitrary impurity concentration. It is found that Eilenberger's well-known results on k2 [Phys. Rev. 153, 584 (1967)] are not correct quantitatively, which are modified appropriately. Calculations are also performed for a two-dimensional system with an isotropic Fermi surface. The results on clean systems differ substantially from those for the three-dimensional system with a spherical Fermi surface. This fact indicates the necessity of considering detailed Fermi-surface structures for a quantitative understanding of the parameters. The coefficient of Δ(r)(Hc2–B)1/2, which is basic to any theoretical evaluation of the thermodynamic and transport properties near Hc2, is obtained accurately.
  • Mermin-Ho vortex in spinor bose-einstein condensates under rotation
    K Machida, T Mizushima, T Kita, T Isoshima
    LASER PHYSICS, 13, 8, 1083, 1090, IOP PUBLISHING LTD, Aug. 2003, [Peer-reviewed]
    English, Scientific journal, It is shown theoretically that the Mermin-Ho vortex is stable in a spinor Bose-Einstein condensate within extended Bogoliubov theory. The phase diagrams for ferromagnetic and antiferromagnetic spinor BEC in a plane of the magnetization of the system and external rotation frequency are calculated. There are several types of vortices with axisymmetry and nonaxisymmetry. Multiple Mermin-Ho vortex configuration is shown to be stable under higher rotation. We also discuss how to create and how to detect the Mermin-Ho vortex.
  • Continuous vortices and collective excitations in ferromagnetic spinor Bose-Einstein condensates
    T Mizushima, K Machida, T Kita
    PHYSICA B-CONDENSED MATTER, 329, 17, 18, ELSEVIER SCIENCE BV, May 2003, [Peer-reviewed]
    English, Scientific journal, Bose-Einstein condensates (BEC) realized in alkali atomic gases with the hyperfine state F = 1 keep "spin" states degenerate and active under an optical trap. These systems, so-called spinor BEC are analogous to the A-phase of the superfluid He-3. Among various topological structures, the Mermin-Ho and Anderson-Toulouse vortices are proposed in superfluid He-3-A phase. We demonstrate by solving the extended Gross-Pitaevskii equation that these topological structures are thermodynamically stable in ferromagnetic spinor BEC under rotation. Furthermore, we show the collective modes for such the vortices within Bogoliubov theory. (C) 2003 Elsevier Science B.V. All rights reserved.
  • Unconventional vortices and phase transitions in rapidly rotating superfluid 3He
    Takafumi Kita
    Physical Review B, 66, 22, 224515, 224515, American Physical Society (APS), 31 Dec. 2002, [Peer-reviewed], [Lead author]
    English, Scientific journal, This paper studies vortex-lattice phases of rapidly rotating superfluid 3He based on the Ginzburg-Landau free-energy functional, where strong-coupling effects are included in the pressure dependence of the fourth-order β parameters. To identify stable phases in the p-Ω plane (p=pressure, Ω=angular velocity), the functional is minimized with the Landau-level expansion method using up to 3000 Landau levels. With nine complex order parameters, this system can sustain various exotic vortices by either (i) shifting vortex cores among different components or (ii) filling in cores with components not used in the bulk. In addition, the phase near the upper critical angular velocity Ωc2 is neither the Balian-Werthamer state nor the Anderson-Brinkman-Morel state, but the polar state with the smallest superfluid density, as already shown by Schopohl. Thus, multiple phases are anticipated to exist in the p-Ω plane. Six different phases are found in the present calculation performed over 0.0001Ωc2<~Ω<~Ωc2, where Ωc2 is of order (1-T/Tc)×107 rad/s. It is shown that the double-core vortex experimentally found in the B phase originates from the conventional hexagonal lattice of the polar state near Ωc2 via (i) a phase composed of interpenetrating polar and Scharnberg-Klemm sublattices, (ii) the A-phase mixed-twist lattice with polar cores, (iii) the normal-core lattice found in the isolated-vortex calculation by Ohmi, Tsuneto, and Fujita, and (iv) the A-phase-core vortex discovered in another isolated-vortex calculation by Salomaa and Volovik. It is predicted that the double-core vortex will disappear completely in the experimental p-T phase diagram to be replaced by the A-phase-core vortex in the angular velocity of order 103–104 rad/s.
  • Spinor Bose-Einstein condensates with many vortices
    T. Kita, T. Mizushima, K. Machida
    Physical Review A, 66, 6, 61601, 61601, American Physical Society (APS), 18 Dec. 2002, [Peer-reviewed], [Lead author]
    English, Scientific journal, Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin F=1 are investigated theoretically based on the Ginzburg-Pitaevskii equations near Tc. The Abrikosov lattice with clear core regions is never found to be stable at any rotation drive Ω. Instead, each component Ψi (i=0,±1) prefers to shift the core locations away from the others to realize almost uniform order-parameter amplitude with complicated magnetic-moment configurations. This system is characterized by many competing metastable structures so that quite a variety of vortices may be realized with a small change in external parameters.
  • Theory of the de Haas–van Alphen effect in type-II superconductors
    Kouji Yasui, Takafumi Kita
    Physical Review B, 66, 18, American Physical Society (APS), 27 Nov. 2002, [Peer-reviewed], [Corresponding author]
    Scientific journal
  • Axisymmetric versus nonaxisymmetric vortices in spinor Bose-Einstein condensates
    T. Mizushima, K. Machida, T. Kita
    Physical Review A, 66, 5, American Physical Society (APS), 12 Nov. 2002, [Peer-reviewed]
    Scientific journal
  • On the Density Matrix of Nonequilibrium Steady-State Statistical Mechanics
    Takafumi Kita
    Journal of the Physical Society of Japan, 71, 8, 1795, 1797, Physical Society of Japan, Aug. 2002, [Peer-reviewed], [Lead author]
    Scientific journal
  • Mermin-Ho Vortex in Ferromagnetic Spinor Bose-Einstein Condensates
    T. Mizushima, K. Machida, T. Kita
    Physical Review Letters, 89, 3, American Physical Society (APS), 25 Jun. 2002, [Peer-reviewed]
    Scientific journal
  • Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors
    Kouji Yasui, Takafumi Kita
    Journal of the Physical Society of Japan, 70, 10, 2852, 2855, Physical Society of Japan, Oct. 2001, [Peer-reviewed], [Corresponding author]
    English, Scientific journal, We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along the extremal orbit is relevant for the magnitude of the extra damping, thereby providing support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which will be useful to estimate angle- and/or band-dependent gap amplitudes.
  • Gauge invariance and Hall terms in the quasiclassical equations of superconductivity
    Takafumi Kita
    Physical Review B, 64, 5, American Physical Society (APS), 29 Jun. 2001, [Peer-reviewed], [Lead author]
    Scientific journal
  • Vortex-Lattice Phases of Superfluid 3He in Rapid Rotation
    Takafumi Kita
    Physical Review Letters, 86, 5, 834, 837, American Physical Society (APS), 29 Jan. 2001, [Peer-reviewed], [Lead author]
    Scientific journal
  • Quasiparticles of d-Wave Superconductors in Finite Magnetic Fields
    Kouji Yasui, Takafumi Kita
    Physical Review Letters, 83, 20, 4168, 4171, American Physical Society (APS), 15 Nov. 1999, [Peer-reviewed], [Corresponding author]
    Scientific journal
  • An Exact Entropy Expression for a Many-Body Problem
    Takafumi Kita
    Journal of the Physical Society of Japan, 68, 11, 3740, 3741, Physical Society of Japan, 15 Nov. 1999, [Peer-reviewed], [Lead author]
    English, Scientific journal
  • Vortex States of the Eu Model for Sr2RuO4
    Takafumi Kita
    Physical Review Letters, 83, 9, 1846, 1849, American Physical Society (APS), 30 Aug. 1999, [Peer-reviewed], [Lead author]
    Scientific journal
  • Solving the Ginzburg-Landau Equations with Magnetic Translation Group
    Takafumi Kita
    Journal of the Physical Society of Japan, 67, 6, 2067, 2074, Physical Society of Japan, 15 Jun. 1998, [Peer-reviewed], [Lead author]
    English, Scientific journal, This paper presents a powerful method to obtain flux-lattice solutionsof the Ginzburg-Landau equations in any external field.A key point lies in expanding the order parameter Ψin a basis consisting of the eigenstates ofthe magnetic translation operators in the mean flux density B.It is shown that retaining a few terms in the expansionprovides practically exact solutions over$0 \lesssim B \leq H_{ { \rm c}2}$.Abrikosov's result near H c2 is obtained hereas a lowest-order approximation.The method clarifies how the higher-Landau-level mixing growsas the field is decreased from H c2.
  • A Microscopic Theory of Abrikosov Lattices. I. Basic Formalism
    Takafumi Kita
    Journal of the Physical Society of Japan, 67, 6, 2075, 2083, Physical Society of Japan, 15 Jun. 1998, [Peer-reviewed], [Lead author]
    English, Scientific journal, This paper generalizesthe method of using the magnetic Bloch states to obtain flux-latticesolutions of the Bogoliubov-de Gennes equations.Developed by several groups,this method has had a limited applicability to the s-wave pairingand to high-κ materials where thespatial variation of the magnetic field may be neglected.It is extended here so that:(i) an arbitrary anisotropic pairing can be handled;(ii) the effect of the screening current can be taken into account.Hence the formalism will enable a fully microscopicdescription of various Abrikosov lattices in clean type-II superconductorsover H c1 ≤H ≤H c2.
  • Angular Momentum of Anisotropic Superfluids at Finite Temperatures
    Takafumi Kita
    Journal of the Physical Society of Japan, 67, 1, 216, 224, Physical Society of Japan, 15 Jan. 1998, [Peer-reviewed], [Lead author]
    English, Scientific journal, With proper care on the boundary conditions,the total orbital angular momentum Lz at finite temperatures is microscopically calculatedfor the Anderson-Brinkman-Morel state in a cylinder with axial symmetry about the z axis,i.e. the textures considered by McClure and Takagi at T=0.The pairing in this geometry occurs between m and 1-m one-particle states, where m denotes the axial quantum number.It is found that Lz decreases from its zero temperature value $\frac{\hbar},{2} {\cal N}$,with N the total particle number, in the same way asthe components of the superfluid density tensor.Responsible for this reduction is identified to be the phase shift between m and 1-m quasiparticle states caused by the difference in the centrifugal potentials.This fact implies that the plane-wave representation is not suitable for the problem.
  • Perturbation Expansion for a Fermi Superfluid. I. Basic Formalism and Angular Momentum
    Takafumi Kita
    Journal of the Physical Society of Japan, 65, 5, 1355, 1372, Physical Society of Japan, 15 May 1996, [Peer-reviewed], [Lead author]
    English, Scientific journal, A theory of a Fermi superfluid is formulated based on the condensate wave function of the configuration space.First, two basic ingredients areextracted from the wave function, i.e. the effective condensate wave function v(x1,x2) and the quasiparticle field γ(x) with xdenoting the space and spin coordinates rα.After transforming a Hamiltonian into a normal-ordered productof γ, a perturbation expansionwith respect to the quasiparticle interaction is formulatedfor both the thermodynamic potential Ωand the one-particle density matrix ρ.The thermodynamic potential thus obtained includes the normal-state expression of Luttinger and Ward as the limit of v→ 0.The density matrix is written as a sum of the coherent part ρ( c)and the quasiparticle part ρ( q),where ρ( c) is expressed only with respect to v(x1,x2).It is shown that v and γ are responsible forthe coherent and thermodynamic properties respectively.Thus the present formalism gives a microscopic foundation for the two-fluid model.Connections with the Gor'kov equations and the Bogoliubov-de Gennes equations are also clarified.It is found that the one-particle density matrices of those formalismsare not equivalent to ρ of the present formalism.The origin of the angular momentum paradox of 3He - Ais traced to this difference.
  • Perturbation Expansion for a Fermi Superfluid. II. Several Equilibrium Properties
    Takafumi Kita
    Journal of the Physical Society of Japan, 65, 5, 1373, 1382, Physical Society of Japan, 15 May 1996, [Peer-reviewed], [Lead author]
    English, Scientific journal, The formalism of the preceding paper is applied to a system of uniform flow.Explicit expressions are obtained for the specific heat: CV,the superfluid-density tensor: ρ, and the spin susceptibility of the singlet pairing: χ.It is the quasiparticle excitation near the excitation thresholdthat is responsible for these quantities.The three expressions for v→0 reduce to the normal-state results of Luttinger;the Leggett expressions of ρ and χare reproduced by neglecting the feedback effects.
  • Real-Space Formalism of the Theory of Superconductivity
    Takafumi Kita
    Journal of the Physical Society of Japan, 65, 4, 908, 911, Physical Society of Japan, 15 Apr. 1996, [Peer-reviewed], [Lead author]
    Scientific journal
  • The Angular Momentum Paradox of 3He-A
    Takafumi Kita
    Journal of the Physical Society of Japan, 65, 3, 664, 666, Physical Society of Japan, 15 Mar. 1996, [Peer-reviewed], [Lead author]
    English, Scientific journal, The kinetic energy of a charged system is calculated for Mermin's one-particledensity matrix of Fermi superfluids. The final expression consistsof two separate contributions from the center-of-mass and the relative motionsof an effective bound-state wave function. The relative part naturally includes coupling of the intrinsic orbital angular momentum densityto the magnetic field.For 3 He-A at T=0, its magnitudeis $(\hbar / 2) \times $(number density),in agreement with Ishikawa's result.
  • Broken Time-Reversal Symmetry of Anisotropic Superfluidity
    Takafumi Kita
    Journal of the Physical Society of Japan, 62, 10, 3539, 3556, Physical Society of Japan, 15 Oct. 1993, [Peer-reviewed], [Lead author]
    English, Scientific journal, Broken time-reversal ($T$) symmetry of anisotropic superfluidity implies topological change of the whole Fermi sphere. An infinite string pierces through the Fermi sphere; the phase of the pair state $|\mbi{k},\ -\mbi{k}\rangle_{\text{s } }$ is multivalued around it; and at $T{=}0$, the one-particle occupation number $n^{(\text{s})}(\mbi{k})$ vanishes on the string. Through these observations, this paper settles the problem of the intrinsic orbital angular momentum in 3He–A: The momentum density at $T{=}0$ is given by $\mbi{g},{=}N_{\text{s } }\mbi{Mv}_{\text{s } }+(1/4)\nabla\times (N_{\text{s } }\hbar\mbi{l})-(\hbar/2)C_{0}\mbi{l}(\mbi{l},{\cdot}\nabla\times\mbi{l})$ with $C_{0},{=}0$, namely, the third term is absent due to $n^{(\text{s})}(\mbi{k}){=}0$ for $\mbi{k},{//}\mbi{l}$. The process reveals that the Green's function approach based on the plane wave expansion fails to describe the topological change. Also, the conclusion raises several basic problems such as the divergence of $H_{\text{c}2}$ for T-breaking superconductivity. Finally, this paper presents a principle connecting the magnetic field with the phase singularity of the wave function. Its implications to the charged-anyon model and the Dirac monopole are also discussed.
  • Superconductivity with two critical temperatures
    Takafumi Kita
    Physical Review B, 48, 6, 3949, 3968, American Physical Society (APS), 01 Aug. 1993, [Peer-reviewed], [Lead author]
    Scientific journal
  • Magnetic properties of the charged Anderson-Brinkman-Morel state: Absence of Hc1
    Takafumi Kita
    Physical Review B, 43, 7, 5343, 5354, American Physical Society (APS), 01 Mar. 1991, [Peer-reviewed], [Lead author]
    Scientific journal
  • New Self-Consistency Relation between the Correlation Energy and the Momentum Distribution Function with Application to the One-Dimensional Hubbard Model
    Yasutami Takada, Takafumi Kita
    Journal of the Physical Society of Japan, 60, 1, 25, 28, Physical Society of Japan, 15 Jan. 1991, [Peer-reviewed]
    Scientific journal
  • Effective-potential expansion method for the many-body problem at finite temperatures. I. Basic formalism
    Yasutami Takada, Takafumi Kita
    Physical Review A, 42, 6, 3242, 3250, American Physical Society (APS), 01 Sep. 1990, [Peer-reviewed]
    Scientific journal
  • Effective-potential expansion method for the many-body problem at finite temperatures. II. Application to a one-dimensional electron system with a repulsive δ-function interaction
    Takafumi Kita, Yasutami Takada
    Physical Review A, 42, 6, 3251, 3258, American Physical Society (APS), 01 Sep. 1990, [Peer-reviewed], [Lead author]
    Scientific journal
  • Magnetic instability in triplet superconductivity
    Takafumi Kita
    Physical Review B, 40, 16, 10816, 10830, American Physical Society (APS), 01 Dec. 1989, [Peer-reviewed], [Lead author]
    Scientific journal
  • Higher-Order Asymptotic Expansion for the Edge Singularities in Metals
    Takafumi Kita
    Journal of the Physical Society of Japan, 56, 12, 4598, 4608, Physical Society of Japan, 15 Dec. 1987, [Peer-reviewed], [Lead author]
    English, Scientific journal, Higher-order coefficients of the asymptotic expansion ($t{\rightarrow}\infty$) for the soft-X-ray-absorption response function $I(t)$ are treated analytically. Based on the model by Mahan and Nozières and de Dominicis, formulation is performed for the coefficient of any order and exact expressions are given for the leading three terms of the series. When transformed into the frequency space, the series of the expansion are expressed in a form with a frequency dependent exponent, which suggests strongly the validity of the generalized power-law formula proposed to surpass the one by Nozières and de Dominicis. For a model conduction band, some numerical examples are presented to show wide applicability of the obtained formula.
  • Edge Singularity and Fano Effect in Metals
    Takafumi Kita, Kazuo Ohtaka, Yukito Tanabe
    Journal of the Physical Society of Japan, 56, 12, 4609, 4626, Physical Society of Japan, 15 Dec. 1987, [Peer-reviewed], [Lead author]
    English, Scientific journal, The X-ray absorption and emission in metals with a localized (resonant) state within the band are treated both analytically and numerically. The model introduced by Kotani and Toyozawa is generalized so as to take into account the scattering of the conduction electrons by the core-hole potential and analyzed by the Fermi golden rule approach. Exact analytic expressions are derived for the line shapes near the threshold and near the localized state while the spectra over the entire frequency range are obtained numerically within an error of 1%. The competition between the edge singularity, the Fano effect and the peak corresponding to the localized state give rise to a variety of the spectral line shapes. In some cases disappearance of the edge singularity due to the Fano effect is shown to be observed.
  • Core Level X-Ray Spectra of Simple Metals:Deviation from the Asymptotic Theory
    Takafumi Kita, Kazuo Ohtaka, Yukito Tanabe
    Journal of the Physical Society of Japan, 56, 1, 387, 407, Physical Society of Japan, 15 Jan. 1987, [Peer-reviewed], [Lead author]
    English, Scientific journal, An analytic treatment is given for the deviations of XAS and XPS intensities from the asymptotic power-law behaviors given by Nozières and de Dominicis (ND). In deriving the formulae, the core-hole potential is assumed to be of contact-type and the energy dependences of physical quantities such as the phase shift and the dispersion integrals are taken into account up to linear terms with respect to the energy. It is shown that the deviations from the asymptotic formulae are expressed by introducing several new quantities which are derived from the first principle. It is also found that the deviations can be incorporated in the framework of the generalized (frequency-dependent) power-law. By comparing with the exact numerical results, the obtained formulae are demonstrated to have much wider applicability in the frequency space than the asymptotic ND formulae.
  • Shapes of R Lines of Cr3+in GdAlO3
    Takafumi Kita, Yukito Tanabe
    Journal of the Physical Society of Japan, 54, 6, 2293, 2303, Physical Society of Japan, 15 Jun. 1985, [Peer-reviewed], [Lead author]
    English, Scientific journal, The line shapes of the optical transition \includegraphics{dummy.eps} of Cr3+ in GdAlO3 are calculated. All the local exchange interactions around the Cr3+ ion, including Gd3+–Gd3+ ones, are taken into account to determine the eigenstate of the $^{4}A_{2}$ state and of the $^{2}E$ state. Possible mechanisms for the transition are considered and selection rules are obtained for each mechanism. From the comparison of the theoretical curves with the experiments, the magnitudes of the Cr3+–Gd3+ exchange integrals are predicted to be $-1.0$ cm-1 for the $^{4}A_{2}$ state and $-0.55$ cm-1 for the $^{2}E$ state. The agreement between the theory and the experiment is fairly good.
  • Ground Configuration of Spins in GdAlO3:Cr
    Takafumi Kita, Yukito Tanabe
    Journal of the Physical Society of Japan, 54, 6, 2304, 2310, Physical Society of Japan, 15 Jun. 1985, [Peer-reviewed], [Lead author]
    English, Scientific journal, The ground configuration of Gd3+ spins with a Cr3+ spin at an Al3+ site is investigated theoretically by treating spins as classical axial vectors. It is found that the eight nearest-neighbour Gd3+ spins around the Cr3+ spin align ferromagnetically or antiferromagnetically, according as the maximum of the molecular field on each Gd3+ site which is caused by the Cr3+–Gd3+ exchange interaction is larger or smaller than that caused by the six Gd3+–Gd3+ ones. The result is interesting in connection with the spectrum of Cr3+ in GdAlO3 below $T_{\text{N } },{=}3.9$ K.

Other Activities and Achievements

Books and other publications

Affiliated academic society

  • 日本物理学会　　　　　　　　　　　　　　　
  • アメリカ物理学会　　　　　　　　　　　　　　　
  • Physical Society of JapanAmerican Physical Society　　　　　　　　　　　　　　　

Research Themes

  • Theoretical Study of Anomalous Long-Range Correlations in Bose Superfluids
    Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
    Apr. 2020 - Mar. 2023
    北 孝文
    第一に、汎関数繰り込み群の手法を臨界点近傍のO(N)模型に適用し、その臨界現象を調べた。N=2の場合はボーズ・アインシュタイン凝縮(BEC)の相転移に対応する。この模型の特徴は、転移点以下の秩序相で南部・ゴールドストーン(NG)・モードが出現して感受率の発散をもたらすことである。したがって、臨界点以下では、秩序変数の相関長は常に発散しており、相関長の臨界指数も定義できない。この事実は、「O(N)模型の臨界指数は転移点の上下で異なっている」ということを強く示唆する。そして、標準的な相転移の教科書に書かれている「相転移点の上下で臨界指数は等しい」との主張は正しくないのではという疑念を抱かせる。そこで、汎関数繰り込み群の手法により、転移点の上下で固定点と臨界指数を独立に調べた。この手法の特徴は、相転移点の上下を同等に解析できることにある。その結果、秩序相でもジョセフソン相関長と呼ばれる相関長が定義できること、しかしその臨界指数は正常相の値とは異なっていることがわかった。また、この臨界指数の非対称性が、自発的対称性の破れによる対称性の変化に由来することも明らかになった。この事実は、教科書の記述とは異なり、臨界指数の非対称性が一般的なものであることを強く示唆している。第二に、BEC相におけるNGモードの性質を、筆者が新たに開発した自己無撞着摂動展開法により解析した。この摂動展開法には、ゴールドストーンの定理を自動的に満足するという望ましい性質がある。その結果、BEC相で現れる3点バーテックスの効果により、NGモードが有限の寿命を持つようになることを明らかにした。また、対応するNGモードのスペクトル関数をボゴリューボフ近似で評価すると、ボゴリューボフ分散が消失してその周りで２ピーク構造を持つことも示した。この事実は、NGモードに関する従来の見解に変革をもたらす可能性を秘めている。
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, Principal investigator, 20K03848
  • Theoretical study of Bose-Einstein condensates using a new self-consistent perturbation expansion
    Grants-in-Aid for Scientific Research
    2010 - 2012
    KITA Takafumi
    A new self-consistent perturbation expansion, which was developed recently by the principal investigator, has been used to clarify basic properties of a single-component Bose-Einstein condensate. A widely accepted viewpoint on the elementary excitations of the system is that the single- and two-particle excitations are identical and described by the gapless excitation of the Bogoliubov theory. We have found, however, that the two excitations are different from each other. It is also found that the well-known expression on the ground-state energy of a dilute Bose gas by Lee, Huang and Yang should be modified due to a new class of Feynman diagrams for the self-energy.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, Principal investigator, Competitive research funding, 22540356
  • Quantitative calculations of response functions of materials andproperties of type-II superconductors
    Grants-in-Aid for Scientific Research(基盤研究(C))
    2006 - 2008
    Takafumi KITA, Takafumi KITA
    熱平衡超伝導電流に対するホール係数の理論的表式を導出し、符号反転の可能性を予言した。第二種超伝導体KOs_2O_6の上部臨界磁場の特徴を理論的に明らかにした。ゴールドストーンの定理と保存則を同時に満足するボーズ・アインシュタイン凝縮相の平均場理論を初めて構成できた。相互作用する量子系の輸送方程式を微視的に導出し、時間発展するエントロピーの表式を得た。
    Ministry of Education, Culture, Sports, Science and Technology, 基盤研究(C), 北海道大学, Principal investigator, Competitive research funding, 18540331
  • NMR Study of peculiar electronic state in the vortex core of anisotrpic superconducttors
    Grants-in-Aid for Scientific Research(基盤研究(A))
    2005 - 2007
    Ken-ichi KUMAGAI, 河本 充司, 古川 裕次, 北 孝文
    In the Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state, a pair-breaking due to a Pauli effect is reduced by the formation of new pairing state(k,-k+q) in the superconducting (SC) state. As a result, a new SC state with spatially-oscillating SC order parameter and spin polarization should appear.[1] A newly-discovered CeCoIn_5 has aroused great interest, as recent measurements revealed that a second order phase transition takes place within the SC state in the vicinity of H_ with H parallel to the ab-plane.[2] Recent experimental results make the FFLO scenario a very appealing one for CeCoI...
    Ministry of Education, Culture, Sports, Science and Technology, 基盤研究(A), 北海道大学, Coinvestigator not use grants, Competitive research funding, 17204027
  • Theoretical study on vortex states in superconductors
    Grants-in-Aid for Scientific Research(基盤研究(C))
    2001 - 2004
    Takafumi KITA
    Theory of the de Haas-van Alphen effect in type-II superconductorsWe performed numerical and analytical studies of the de Haas-van Alphen oscillation in type-II superconductors. We derived an analytic formula for the extra attenuation observed in the vortex state, which can also be used to estimate the band and/or angle dependent gap anisotropy. Using it, we estimated gap amplitude of several materials.Vortex structures of superfluid ^3He and spinor Base-Einstein condensatesBased on the Ginzburg-Landau equations near the transition temperature, we performed a theoretical study on the vortex...
    Ministry of Education, Culture, Sports, Science and Technology, 基盤研究(C), 北海道大学, Principal investigator, Competitive research funding, 13640341
  • 渦糸状態の微視的解明をめざして-異方的超伝導体の理論的研究
    科学研究費補助金(基盤研究(C))
    1999 - 2000
    北 孝文
    (1)UPt_3とSr_2RuO_4の渦糸状態の理論的解明これら2つの物質、特にUPt_3では、二つ以上のオーダー・パラメータを持つ超伝導状態が出現している可能性が高い。Landau準位展開法により、これらの物質に対するGL方程式を全磁場領域で精度よく解いた。そして、コアの無い全く新しい渦糸状態が実現される可能性のあることを指摘した。この新たな渦糸状態は、2ピーク構造という特徴的な磁場分布を持ち、NMRやμSRの実験で検証することができる。すでにいくつかのグループにより実験が始まっており、観測されれば全く新しい渦糸状態の発見となる。(2)d波超伝導体の準粒子状態とSTMスペクトルd_波とs波超伝導体についてBdG方程式をLandau準位展開法で数値的に解き、低磁場領域における両者の準粒子状態の詳細・違いを明らかにした。D_波はBi_2Sr_2CaCu_2O_8_+_δ等の高温超伝導体で実現されており、その渦糸中心の準粒子状態には理論・実験両面から大きな関心が寄せられている。計算の結果、d_波の低エネルギー準粒子が磁気ブリルアン領域内で大きな分散を持ち、束縛状態が無いことが確認できた。また渦糸中心でのSTMスペクトルを計算し、YB_2Cu_3O_7_-_δの実験結果を定性的に説明できることを明らかにした。さらに、d_文部科学省, 基盤研究(C), 北海道大学, Principal investigator, Competitive research funding, 11640328
  • 時間反転対称性の破れた超伝導体の理論的研究
    科学研究費補助金(奨励研究(A))
    1994 - 1994
    北 孝文
    この1年間の研究により、すべての粒子が実空間(r空間)で二粒子束縛状態を作っている、という描像から出発した超伝導理論の定式化をほぼ終えることができ、論文にまとめる段階まで来ている。この定式化の特徴は、以下の3点にある。1.BCS理論の結論をある極限において再現する。2.多体相関の効果を、normal stateと同様の摂動展開により系統的に取り組むことができる。3.絶対零度での超流動^3He-Aの軌道角運動量が、(N/2)hであると予言する。3については、既成の理論、すなわちゴルコフ方程式との違いがどこにあるのかも明らかにすることができた。以上のように、当初の研究目標の重要な部分について、成果を上げることができたと思っている。これからの課題は、この定式化がどこまで既成の理論と同じ結果を与え、どのような場合に異なる結果を与えるのかを明らかにし、また、その違いを明白にする実験を見い出すことである。BCS理論が発表されてすでに40年近く経つが、超流動・超伝導理論の一層の発展のためには、理論の再検討・より確固とした基礎づけが必要である。いましばらくの時間を、この目的に費やしたいと思っている。
    文部科学省, 奨励研究(A), 北海道大学, Principal investigator, Competitive research funding, 06740268
  • 超伝導と超流動，輸送現象　　　　　　　　　　　　　　　
    Competitive research funding
  • Superconductivity, Superfluidity, Transport Theory　　　　　　　　　　　　　　　
    Competitive research funding

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