Tadahiro Miyao |

Faculty of Science Mathematics Mathematics |

Associate Professor |

Last Updated :2020/09/10

- 20554421

- 2012/04 - Today Hokkaido University School of Science, Mathematics
- 2009/04 - 2012/03 Setsunan University Faculty of Science and Engineering
- 2008/04 - 2009/03 ミュンヘン工科大学 数学センター ポスドク
- 2005/04 - 2008/03 日本学術振興会 特別研究員
- 2005/04 - 2006/11 ミュンヘン工科大学 数学センター ポスドク
- 2004 - 2005 Hokkai-Gakuen University Faculty of Engineering

**Note on the Retarded van der Waals Potential within the Dipole Approximation**Tadahiro MiyaoSymmetry, Integrability and Geometry: Methods and Applications (SIGMA) 16 (036) 2020/05 [Refereed][Not invited]**Correlation Inequalities for Schrödinger Operators.**Tadahiro MiyaoMathematical Physics, Analysis and Geometry 23 (3) 2020 [Refereed][Not invited]**Stability of Ferromagnetism in Many-Electron Systems.**Tadahiro MiyaoJournal of Statistical Physics 176 1211 - 1271 2019 [Refereed][Not invited]- Miyao TadahiroJournal of Functional Analysis 276 (6) 1948‐1977 0022-1236 2019 [Refereed][Not invited]
**Ground state properties of the Holstein-Hubbard model**Tadahiro MiyaoAnnales Henri Poincar´e 19 2543 - 2555 2018 [Refereed][Not invited]- Tadahiro MiyaoANNALES HENRI POINCARE 18 (9) 2849 - 2871 1424-0637 2017/09 [Refereed][Not invited]

Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field. - Tadahiro MiyaoANNALES HENRI POINCARE 18 (1) 193 - 232 1424-0637 2017/01 [Refereed][Not invited]

The Holstein model has widely been accepted as a model comprising electrons interacting with phonons; analysis of this model's ground states was accomplished two decades ago. However, the results were obtained without completely taking repulsive Coulomb interactions into account. Recent progress has made it possible to treat such interactions rigorously; in this paper, we study the Holstein-Hubbard model with repulsive Coulomb interactions. The ground-state properties of the model are investigated; in particular, the ground state of the Hamiltonian is proven to be unique for an even number of electrons on a bipartite connected lattice. In addition, we provide a rigorous upper bound on charge susceptibility. - Tadahiro MiyaoJOURNAL OF STATISTICAL PHYSICS 165 (2) 225 - 245 0022-4715 2016/10 [Refereed][Not invited]

This study investigated the extended Holstein-Hubbard model at half-filling as a model for describing the interplay of electron-electron and electron-phonon couplings. When the electron-phonon and nearest-neighbor electron-electron interactions are strong, we prove the existence of long-range charge order in three or more dimensions at a sufficiently low temperature. As a result, we rigorously justify the phase competition between the antiferromagnetism and charge orders. - Tadahiro MiyaoJOURNAL OF STATISTICAL PHYSICS 164 (2) 255 - 303 0022-4715 2016/07 [Refereed][Not invited]

We present a general framework of Griffiths inequalities for quantum systems. Our approach is based on operator inequalities associated with self-dual cones and provides a consistent viewpoint of the Griffiths inequality. As examples, we discuss the quantum Ising model, quantum rotor model, Bose-Hubbard model, and Hubbard model. We present a model-independent structure that governs the correlation inequalities. - Tadahiro MiyaoLETTERS IN MATHEMATICAL PHYSICS 105 (8) 1119 - 1133 0377-9017 2015/08 [Refereed][Not invited]

We extend the Kubo-Kishi theorem concerning the charge susceptibility of the Hubbard model in the following way: (i) The electron-photon interaction is taken into account. (ii) Not only on-site but also general Coulomb repulsions are considered. - Tadahiro MiyaoREPORTS ON MATHEMATICAL PHYSICS 74 (3) 379 - 398 0034-4877 2014/12 [Refereed][Not invited]

In condensed matter physics, the polaron is described by the Hamiltonian of H. Frohlich. In this paper, the Frohlich Hamiltonian is investigated from a viewpoint of operator inequalities proposed in [36]. This point of view clarifies the monotonicity of polaron energy, i.e. denoting the lowest energy of the Frohlich Hamiltonian with the ultraviolet cutoff A by EA, we prove that E-Lambda > E-Lambda' for Lambda < Lambda'. - Tadahiro MiyaoJOURNAL OF STATISTICAL PHYSICS 153 (1) 70 - 92 0022-4715 2013/10 [Refereed][Not invited]

We construct a general theory of operator monotonicity and apply it to the Frohlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Frohlich model. - Tadahiro MiyaoJOURNAL OF STATISTICAL PHYSICS 149 (3) 519 - 550 0022-4715 2012/11 [Refereed][Not invited]

Ground state properties of the SSH model are studied. In particular, the uniqueness of the ground state is proven. As a consequence, characteristic spin structure of the ground state is revealed. - Tadahiro Miyao, Herbert SpohnJOURNAL OF MATHEMATICAL PHYSICS 53 (9) 095215-095215-15 0022-2488 2012/09 [Refereed][Not invited]

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit alpha -> 0 together with the relative distance between the atoms increasing as alpha(-gamma) R, gamma > 0. In particular we determine explicitly the crossover function from the R-6 van der Waals potential to the R-7 retarded van der Waals potential, which takes place at scale alpha R-2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4745911] - Tadahiro MiyaoJOURNAL OF STATISTICAL PHYSICS 147 (2) 436 - 447 0022-4715 2012/04 [Refereed][Not invited]

The one-dimensional Holstein-Hubbard model is studied. We show the uniqueness of the ground state and the ordering of energy levels. - Tadahiro MiyaoREVIEWS IN MATHEMATICAL PHYSICS 23 (7) 749 - 822 0129-055X 2011/08 [Refereed][Not invited]

The self-dual cone - the central object of this review - is introduced. Several operator inequalities associated with the self-dual cone are defined and mathematical properties of those are investigated. In general there are infinitely many choices of self-dual cones in a Hilbert space. Each of these lead to a distinct family of operator inequalities in the Hilbert space which enables us to analyze quantum physical models with respect to several aspects. We refer to these applications as self-dual cone analysis. The focus of this review lies on the self-dual cone analysis of models in condensed matter physics. In particular, by taking a physically proper self-dual cone, the interaction term of the Hamiltonian of the system becomes attractive from a viewpoint of our new operator inequalities. This attractive term enables us to analyze the system and various aspects of physical interest in detail. For instance, if the attractive term is ergodic, it is shown that the ground state is unique. By the uniqueness and the conservation laws, the physically symmetric state is realized as the ground state. This could be regarded as a physical order. As applications, the BCS model and the one-dimensional Frohlich model are studied. We explain, from a viewpoint of the self-dual cone analysis, the appearance of macroscopic phase angles in the superconductors, Josephson effect and the Peierls instability. **Nondegeneracy of ground states in the nonrelativistic quantum ﬁeld theory**Tadahiro MiyaoJournal of Operator Theory 64 207 - 241 2010 [Refereed][Not invited]**Time reversal symmetries and properties of ground states in nonrelativistic QED**Tadahiro MiyaoRIMS Kokyuroku Bessatsu B21 35 - 44 2010 [Refereed][Not invited]- Tadahiro MiyaoMONATSHEFTE FUR MATHEMATIK 157 (4) 365 - 378 0026-9255 2009/08 [Refereed][Not invited]

We introduce the polaron model with at most one phonon from the H. Frohlich polaron Hamiltonian by eliminating contributions from more than two phonons. Spectral properties of this 0,1-phonon polaron model are investigated. It is clarified that, in the weak coupling region, the lowest energy and the effective mass obtained from the 0,1-phonon polaron model agree with those of the H. Frohlich polaron Hamiltonian. - Tadahiro Miyao, Herbert SpohnJOURNAL OF MATHEMATICAL PHYSICS 50 (7) 072103 0022-2488 2009/07 [Refereed][Not invited]

The retarded van der Waals potential, as first obtained by Casimir and Polder, is usually computed on the basis of nonrelativistic quantum electrodynamics . The Hamiltonian describes two infinitely heavy nuclei, charge e, separated by a distance R and two spinless electrons, charge -e, nonrelativistically coupled to the quantized radiation field. Casimir and Polder used the dipole approximation and small coupling to the Maxwell field. We employ here the full Hamiltonian and determine the asymptotic strength of the leading -R(-7) potential, which is valid for all e. Our computation is based on a path integral representation and expands in 1/R, rather than in e. - Michael Loss, Tadahiro Miyao, Herbert SpohnLETTERS IN MATHEMATICAL PHYSICS 89 (1) 21 - 31 0377-9017 2009/07 [Refereed][Not invited]

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated. - Tadahiro Miyao, Herbert SpohnJOURNAL OF FUNCTIONAL ANALYSIS 256 (7) 2123 - 2156 0022-1236 2009/04 [Refereed][Not invited]

We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as H(P), P is an element of R(3). We study the spectrum of H(P). In particular we prove that, for non-zero photon mass, the ground state is exactly two-fold degenerate and separated by a gap, uniformly in P, from the rest of the spectrum. (c) 2008 Elsevier Inc. All rights reserved. - Michael Loss, Tadahiro Miyao, Herbert SpohnJOURNAL OF FUNCTIONAL ANALYSIS 243 (2) 353 - 393 0022-1236 2007/02 [Refereed][Not invited]

Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and N electrons coupled to the radiation field. Since the total momentum P is conserved, the Hamiltonian H admits a fiber decomposition with respect to P with fiber Hamiltonian H(P). A stable atom, respectively ion, means that the fiber Hamiltonian H(P) has an eigenvalue at the bottom of its spectrum. We establish the existence of a around state for H(P) under (i) an explicit bound on P, (ii) a binding condition, and (iii) an energy inequality. The binding condition is proven to hold for a heavy nucleus and the energy inequality for spinless electrons. (C) 2006 Published by Elsevier Inc. **Nonrelativistic limit of the abstract chiral quark soliton model and conﬁning eﬀects**Tadahiro MiyaoJournal of Operator Theory 57 429 - 441 2007 [Refereed][Not invited]**Lowest energy states in nonrelativistic QED: atoms and ions in motion**Michael Loss, Tadahiro Miyao, Herbert SpohnJournal of Functional Analysis 34 689 - 717 2007 [Refereed][Not invited]- Tadahiro Miyao, Herbert SpohnANNALES HENRI POINCARE 8 (7) 1333 - 1370 1424-0637 2007 [Refereed][Not invited]

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Frohlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar-Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large. - Tadahiro MiyaoHokkaido Mathematical Journal 34 (1) 159 - 184 0385-4035 2005 [Refereed][Not invited]

Considered is a quantum system of N (≥ 2) charged particles moving in the plane R2 under the influence of a perpendicular magnetic field concenrated on the positions where the particle exsists. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the momentum operators with a winding gauge potential are investigated. The momentum operators with a winding gauge potential are represented by the fibre direct integral of Arai’s momentum operators [1]. Using this fibre direct integral decomposition, commutation properties of the momentum operators are investigated. A notion of local quantization of the magnetic flux is introduced to characterize the strong commutativity of the momentum operators. Aspects of the representation of the canonical commutation relations (CCR) are discussed. There is an interesting relation between the representation of the CCR with respect to this system and Arai’s representation. Some applications of those results are also discussed. © 2005 by the University of Notre Dame. All rights reserved. **Dirac-Weyl operators with a winding gauge potential**Tadahiro MiyaoHokkaido Mathematical Journal 34 185 - 214 2005 [Refereed][Not invited]**Stability of discrete ground state**Tadahiro Miyao, Itaru SasakiHokkaido Mathematical Journal 34 185 - 214 2005 [Refereed][Not invited]- T MiyaoINTEGRAL EQUATIONS AND OPERATOR THEORY 50 (4) 505 - 535 0378-620X 2004/12 [Refereed][Not invited]

We introduce the notion of strong supercommutativity of self-adjoint operators on a Z(2)-graded Hilbert space and give some basic properties. We clarify that strong supercommutativity is a unification of strong commutativity and strong anticommutativity. We also establish the theory of super quantization. Applications to supersymmetric quantum field theory and a fermion-boson interaction system are discussed.

- Tadahiro Miyao Oberwolfach report 55- 42 -45 2018 [Not refereed][Invited]
**Reflection positivity and operator theoretic correlaion inequalities** - Tadahiro Miyao RIMS Kokyuroku 2010- 127 -131 2016 [Not refereed][Invited]
**Correlation inequalities for the Fro¨hlich model** - 宮尾 忠宏 数理解析研究所講究録 1961- 12 -16 2015/08 [Not refereed][Invited]
- Miyao Tadahiro RIMS Kokyuroku 1904- 46 -53 2014/07 [Not refereed][Invited]
- Miyao Tadahiro RIMS Kokyuroku 1563- 109 -123 2007/06 [Not refereed][Invited]

- Analytic Studies開講年度 : 2018課程区分 : 修士課程開講学部 : 理学院キーワード : 臨界現象，繰り込み群，Gibbs状態，DLR方程式，Ising模型，Dysonの階層模型，φ^4模型，相関関数
- Analysis F開講年度 : 2018課程区分 : 学士課程開講学部 : 理学部キーワード : 確率空間，確率変数，分布関数，期待値，分散，母関数，特性関数，法則収束，中心極限定理，独立性，条件つき確率／期待値，確率収束，大数の弱法則，概収束，大数の強法則．
- Advanced Mathematical Analysis開講年度 : 2018課程区分 : 学士課程開講学部 : 理学部キーワード : 臨界現象，繰り込み群，Gibbs状態，DLR方程式，Ising模型，Dysonの階層模型，φ^4模型，相関関数
- Calculus I開講年度 : 2018課程区分 : 学士課程開講学部 : 全学教育キーワード : 数列，収束，関数，極限，微分，偏微分，テイラ－の定理
- Calculus I開講年度 : 2018課程区分 : 学士課程開講学部 : 全学教育キーワード : 数列, 収束, 関数, 極限, 微分, 偏微分, テイラ－の定理
- Calculus II開講年度 : 2018課程区分 : 学士課程開講学部 : 全学教育キーワード : 原始関数, 積分, 重積分, リ－マン和, 変数変換