研究者データベース
Last Updated :2024/07/03
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プロフィール情報
学位
プロフィール情報
姓
宮尾, ミヤオ名
忠宏, タダヒロID各種
201301003306158953
対象リソース
業績リスト
研究キーワード
研究分野
経歴
- 2022年04月 - 現在 北海道大学 大学院理学研究院 教授
- 2012年04月 - 2022年03月 北海道大学 理学部 数学科 准教授
- 2009年04月 - 2012年03月 摂南大学 理工学部 講師
- 2008年04月 - 2009年03月 ミュンヘン工科大学 数学センター ポスドク
- 2005年04月 - 2008年03月 日本学術振興会 特別研究員
- 2005年04月 - 2006年11月 ミュンヘン工科大学 数学センター ポスドク
- 2004年 - 2005年 北海学園大学 工学部 非常勤講師
学歴
委員歴
論文
- Tadahiro Miyao, Hayato TominagaAnnals of Physics 169381 - 169381 2023年06月 [査読有り][通常論文]
- Tadahiro Miyao, Kazuhiro Nishimata, Hayato TominagaQuantum Studies: Mathematics and Foundations 2022年12月21日 [査読有り][通常論文]
- Tadahiro Miyao, Hayato TominagaAnnals of Physics 168467 - 168467 2021年04月 [査読有り]
- Tadahiro MiyaoAnnales Henri Poincaré 21 12 4027 - 4072 2020年12月 [査読有り]
- Tadahiro MiyaoSymmetry, Integrability and Geometry: Methods and Applications 2020年04月26日 [査読有り]
- Tadahiro MiyaoMathematical Physics, Analysis and Geometry 23 1 2020年03月 [査読有り]
- Tadahiro MiyaoJournal of Statistical Physics 176 5 1211 - 1271 2019年09月 [査読有り]
- Miyao TadahiroJournal of Functional Analysis 276 6 1948‐1977 2019年 [査読有り][通常論文]
- Tadahiro MiyaoAnnales Henri Poincaré 19 8 2543 - 2555 2018年08月 [査読有り]
- 宮尾忠宏Annales Henri Poincar´e 18 9 2849 - 2871 2017年09月 [査読有り][通常論文]
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 2017年01月 [査読有り][通常論文]
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. - 宮尾忠宏Journal of Statistical Physics 165 2 225 - 245 2016年10月 [査読有り][通常論文]
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. - 宮尾忠宏Journal of Statistical Physics 164 2 255 - 303 2016年07月 [査読有り][通常論文]
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. - 宮尾忠宏Letters in Mathematical Physics 105 8 1119 - 1133 2015年08月 [査読有り][通常論文]
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 2014年12月 [査読有り][通常論文]
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 2013年10月 [査読有り][通常論文]
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 2012年11月 [査読有り][通常論文]
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 2012年09月 [査読有り][通常論文]
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 2012年04月 [査読有り][通常論文]
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 2011年08月 [査読有り][通常論文]
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宮尾忠宏Journal of Operator Theory 64 207 - 241 2010年 [査読有り][通常論文]
- 宮尾忠宏RIMS Kokyuroku Bessatsu B21 35 - 44 京都大学 2010年 [査読有り][通常論文]
- Tadahiro MiyaoMONATSHEFTE FUR MATHEMATIK 157 4 365 - 378 2009年08月 [査読有り][通常論文]
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 2009年07月 [査読有り][通常論文]
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 2009年07月 [査読有り][通常論文]
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 2009年04月 [査読有り][通常論文]
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 2007年02月 [査読有り][通常論文]
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宮尾忠宏Journal of Operator Theory 57 429 - 441 2007年 [査読有り][通常論文]
- Tadahiro Miyao, Herbert SpohnANNALES HENRI POINCARE 8 7 1333 - 1370 2007年 [査読有り][通常論文]
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 2005年 [査読有り][通常論文]
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. - Tadahiro MiyaoHokkaido Mathematical Journal 34 1 185 - 218 2005年 [査読有り][通常論文]
Considered is a quantum system of N (≥ 2) charged particles moving in the plane R2 under the influence of a perpendicular magnetic field. Each particle feels the magnetic field concenrated on the positions of the other particles. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the Dirac-Weyl operators with a winding gauge potential are investigated. Notions of local quantization and partial quantization are introduced to determine them. Especially, it is proven that existence of the zero-energy states of the Dirac-Weyl operators with a winding gauge potential is well determined by the local quantization and the partial quantization. © 2005 by the University of Notre Dame. All rights reserved. - Tadahiro Miyao, Itaru SasakiHokkaido Mathematical Journal 34 3 689 - 717 2005年 [査読有り][通常論文]
We present new criteria for a self-adjoint operator to have a ground state. Although the proof which we give is easy, it has many applications. And in various models, it is easy to check the criteria. As an application, we consider models of “quantum particles” coupled to a massive Bose field and prove the existence of a ground state of them, where the particle Hamiltonian does not necessarily have compact resolvent. © 2005 by the University of Notre Dame. All rights reserved. - T MiyaoINTEGRAL EQUATIONS AND OPERATOR THEORY 50 4 505 - 535 2004年12月 [査読有り][通常論文]
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.
MISC
- Reflection positivity and operator theoretic correlaion inequalities宮尾忠宏 Oberwolfach report 55 42 -45 2018年 [査読無し][招待有り]
- 宮尾 忠宏 数理解析研究所講究録 (2010) 127 -131 2016年12月
- Correlation inequalities for the Fro¨hlich model宮尾忠宏 数理解析研究所考究録 2010 127 -131 2016年 [査読無し][招待有り]
- 宮尾 忠宏 数理解析研究所講究録 1904 46 -53 2014年07月 [査読無し][招待有り]
- 宮尾 忠宏 数理解析研究所講究録 1563 109 -123 2007年06月 [査読無し][招待有り]
所属学協会
共同研究・競争的資金等の研究課題
- 日本学術振興会：科学研究費助成事業研究期間 : 2018年04月 -2023年03月代表者 : 宮尾 忠宏近藤格子模型で記述される電子系とフォノンが相互作用する系の基底状態の磁気特性を解析した．その結果，近藤格子系の基底状態の磁気特性は，フォノンとの相互作用がある程度小さければ安定であることを証明した．さらに，基底状態におけるスピン2点相関関数の性質も解析した．これまでに近藤格子系とフォノンの相互作用に関する厳密な解析は為されておらず，ここで得られた結果は，筆者が提唱する作用素論不等式理論が多電子系の厳密解析において有効であることを例証したと見做せる．
この研究で得られた解析と，筆者の過去の解析結果を総合することにより，多電子系の基底状態の磁気特性の安定性を記述する一般論を，富田-竹崎理論を用いて構成した．このような統一的な視点はこれまでになかったものであり，今後の発展が十分に期待できる．実際，この理論から派生した，新しいプロジェクトが現在進行中である．
上述の結果とは独立に，SU(n) Hubbard模型に関する解析を行った．通常のSU(2) Hubbard模型で良く知られている，Aizenman-Liebの定理とは，Nagaoka-Thoulessの定理の有限温度版であると言われている．筆者はAizenman-Liebの定理をSU(n) Hubbard模型に拡張した．ここで用いられた解析手法は，分配関数の経路積分表示を基にしたランダムループ展開であり，通常のスピン系におけるランダムループ展開に比較してその取扱いが難しい．SU(n)ハバード模型に関する厳密な結果は少なく，ここで得られた結果を基に，この模型に対する新しいプロジェクトを準備している最中である． - 日本学術振興会：科学研究費助成事業研究期間 : 2016年04月 -2020年03月代表者 : 廣島 文生, 宮尾 忠宏A. ラフパス理論によるGibbs測度の構成と応用、B. 基底状態の研究、C. 確率解析的UVくりこみ理論、D. 多様体上の場の量子論の研究、E. 場の量子論におけるSDEと古典極限の研究。さらに隔年ごとに場の量子論のスペクトル解析に関する国際研究集会を開催した。 AとCに関しては大きな進展があり、論文としてまとめた。Bについても結果をまとめ論文として完成させた。Eについては共同研究が始まり現在研究継続中である。国際研究集会の開催に関しては毎年旅費などをサポートすることができた。
- 日本学術振興会：科学研究費助成事業研究期間 : 2013年04月 -2016年03月代表者 : 宮尾 忠宏（１）自己双対錘を不変にする作用素のなす不等式を応用することにより、フレーリッヒ模型の紫外切断除去の新しい方法を開発した。これにより、紫外切断を除去した模型の基底状態が一意的であることの初めての証明を与えた。この結果は、国際的な雑誌に論文として掲載されている。 （２）多電子と量子電磁場が相互作用する系の電荷感受率の上界を評価した。これにより、考察下の系において電荷長距離秩序が存在しないことを厳密に証明した。この結果は国際的な雑誌に論文として掲載されている。
- 日本学術振興会：科学研究費助成事業研究期間 : 2011年 -2013年代表者 : 伊東 恵一, 寺本 恵昭, 宮尾 忠宏, 田村 博志, 廣川 真男, 廣島 文生くりこみ群を用いて、前世紀からの難問の解決を目指す.代表的な問題は, ミレニアム問題としてクレイ研究所の懸賞問題として挙げられ, 最近話題になったペレルマンによる, ポアンカレ予想の解決, ワイルズによるフェルマー問題の解決などがある. ナヴィエ・ストークス方程式の乱流解, ヤング・ミルズ・ゲージ理論の存在などが未解決であり,共通して積分が無限次元という困難がある.これを関数空間の中に部分空間列を捜し（軌道という）これに沿って行う手法で解決する. ゲージ理論のプロトタイプの２次元非線形スピンモデルでほぼ解決を見た。
- 日本学術振興会：科学研究費助成事業研究期間 : 2011年 -2012年代表者 : 宮尾 忠宏ヒルベルト空間における自己双対錐から自然に導かれる作用素不等式の性質を調べ、その結果を固体物理学におけるいくつかのモデルに適用した。応用例としてHolstein-Hubbardmodel、SSHmodel、Frohlichmodelが挙げられる。具体的に得た結果は、1次元Holstein-HubbardmodelやSSHmodelにおいて、基底状態が一意になること、その結果として、基底状態の磁気的な特性が明らかなったことが挙げられる。