Universality of Random Matrices and Semiclassical Quantum Theory

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540372
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Nagoya University
• Principal Investigator: NAGAO Taro Nagoya University, 大学院・多元数理科学研究科, 教授 (10263196)
• Project Period (FY): 2008 – 2012
• Keywords: ランダム行列 / 半古典量子論

Research Abstract

ランダム行列理論の応用において重要な普遍性の理解を深める。そのために、行列サイズが大きい極限におけるランダム行列の振る舞いについて、直交多項式の方法などを用いて調べる。また、量子カオス系や複雑ネットワークにおける普遍性の成り立ちを明らかにするために、半古典量子論や場の理論的な方法を用いた解析を進める。

Research Products

• [Journal Article] Chaotic transport in the symmetry crossover regime with a spin-orbit interaction (2010)
  • Author(s): Keiji Saito, Taro Nagao
  • Journal Title: Phys.Rev.B 82巻 Pages: 125322
  • Peer Reviewed
• [Journal Article] Semiclassical theory for universality in quantum chaos with symmetry crossover (2009)
  • Author(s): Keiji Saito, Taro Nagao, Sebastian Muller, Petr Braun
  • Journal Title: J.Phys.A : Math.Theor. 42巻 Pages: 495101
  • Peer Reviewed
• [Journal Article] The n-level spectral correlations for chaotic systems (2009)
  • Author(s): Taro Nagao, Sebastian Muller
  • Journal Title: J.Phys.A : Math.Theor. 42巻 Pages: 375102
  • Peer Reviewed
• [Journal Article] Skeworthogonal polynomials and the partly symmetric real Ginibre ensemble (2008)
  • Author(s): Peter J. Forrester, Taro Nagao
  • Journal Title: J.Phys.A : Math.Theor. 41巻 Pages: 375003
  • Peer Reviewed
• [Presentation] 実非対称ランダム行列の固有値分布 (2012)
  • Author(s): 永尾太郎
  • Organizer: 日本数学会2010年度秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2012-09-22
• [Presentation] スピン系の量子輸送と球面上のブラウン運動 (2010)
  • Author(s): 永尾太郎
  • Organizer: ランダム作用素のスペクトルと関連する話題
  • Place of Presentation: 慶慮義塾大学
  • Year and Date: 2010-12-09
• [Presentation] Determinantal spectral correlations for chaotic systems (2009)
  • Author(s): Taro Nagao
  • Organizer: Workshop "Spectra of random operators and related topics
  • Place of Presentation: 京都大学
  • Year and Date: 2009-12-03
• [Presentation] Spectral density of the adjacency matrices of complex networks (2008)
  • Author(s): 永尾太郎
  • Organizer: ランダム作用素のスペクトルと関連する話題
  • Place of Presentation: 京都大学
  • Year and Date: 2008-11-27
• [Presentation] Eigenvalue correlations for the real Ginibre ensemble (2008)
  • Author(s): Taro Nagao
  • Organizer: Workshop on "Random matrices, special functions and related topics
  • Place of Presentation: 京都大学
  • Year and Date: 2008-11-14
• [Presentation] Vicious walks and matrix models (2008)
  • Author(s): Taro Nagao
  • Organizer: Workshop on "Random tilings, random partitions and stochastic growth processes
  • Place of Presentation: Universite de Montreal
  • Year and Date: 2008-09-03