Universality of Random Matrices and Semiclassical Quantum Theory

• 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 名古屋大学, 多元数理科学研究科, 教授 (10263196)
• Co-Investigator(Renkei-kenkyūsha): TATE Tatsuya 名古屋大, 大学院・多元数理科学研究科, 准教授 (00317299) ; SAITO Keiji 慶應義塾大学, 理工学部, 准教授 (90312983)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: ランダム行列 / 半古典量子論

Research Abstract

The eigenvalue correlation functions for the matrix ensemble continuously interpolating between the asymmetric real and symmetric real random matrices were evaluated and the asymptotic behavior in the limit of large matrix dimension was derived. The method of semiclassical diagrammatic expansion was applied to classically chaotic quantum systems and the universal properties were reproduced. The random matrix methods were applied to the theory of complex networks and the eigenvalue densities of the matrices describing the networks were shown to be analytically evaluated in the limit of large average degree.

Research Products

• [Journal Article] Spectral density of complex networks with two species of nodes (2013)
  • Author(s): Taro Nagao
  • Journal Title: J. Phys. A: Math. Theor. Volume: 46巻 Pages: 65003-65003
  • Peer Reviewed
• [Journal Article] Spectral density of complex networks with two species of nodes (2013)
  • Author(s): Taro Nagao
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 46 Issue: 6 Pages: 65003-65003
  • DOI: 10.1088/1751-8113/46/6/065003
  • Peer Reviewed
• [Journal Article] Parametric correlations versus fidelity decay: the symmetry breaking case (2011)
  • Author(s): Heiner Kohler, Taro Nagao and Hans-Jurgen Stockmann
  • Journal Title: Phys. Rev. E Volume: 84巻 Pages: 61133-61133
  • Peer Reviewed
• [Journal Article] Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition (2011)
  • Author(s): Gernot Akemann and Taro Nagao
  • Journal Title: J. High Energy Phys. Volume: 2011巻 Pages: 60-60
  • Peer Reviewed
• [Journal Article] Determinantal correlations for classical projection processes (2011)
  • Author(s): Peter J. Forrester and Taro Nagao
  • Journal Title: J. Stat. Mech. Volume: 2011巻
  • Peer Reviewed
• [Journal Article] Spectral correlation functions for chaotic systems (2011)
  • Author(s): Taro Nagao
  • Journal Title: 京都大学数理解析研究所講究録別冊,"Spectra of Random Operators and Related Topics" (ed. by N. Minami) Volume: B27巻 Pages: 99-99
  • Peer Reviewed
• [Journal Article] Spectral correlation functions for chaotic systems (2011)
  • Author(s): Taro Nagao
  • Journal Title: 京都大学数理解析研究所講究録別冊 Volume: B27 Pages: 99-114
  • Peer Reviewed
• [Journal Article] Determinantal correlations for classical projection processes (2011)
  • Author(s): Peter J.Forrester, Taro Nagao
  • Journal Title: J.Stat.Mech. Volume: 2011 Issue: 08 Pages: P08011-P08011
  • DOI: 10.1088/1742-5468/2011/08/p08011
  • Peer Reviewed
• [Journal Article] Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition (2011)
  • Author(s): Gernot Akemann, Taro Nagao
  • Journal Title: J.High Energy Phys. Volume: 2011 Issue: 10
  • DOI: 10.1007/jhep10(2011)060
  • Peer Reviewed
• [Journal Article] Parametric correlations versus fidelity decay: the symmetry breaking case (2011)
  • Author(s): Heiner Kohler, Taro Nagao, Hans-Jurgen Stockmann
  • Journal Title: Phys.Rev.E Volume: 84 Issue: 6
  • DOI: 10.1103/physreve.84.061133
  • Peer Reviewed
• [Journal Article] Chaotic transport in the symmetry crossover regime with a spin-orbit interaction (2010)
  • Author(s): Keiji Saito and Taro Nagao
  • Journal Title: Phys. Rev. B Volume: 82巻 Pages: 125322-125322
  • Peer Reviewed
• [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: 125322-125322
  • Peer Reviewed
• [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 Volume: 182 Pages: 125322-125322
  • Peer Reviewed
• [Journal Article] Semiclassical theory for universality in quantum chaos with symmetry crossover (2009)
  • Author(s): Keiji Saito, Taro Nagao, Sebastian Muller and Petr Braun
  • Journal Title: J. Phys. A: Math. Theor. Volume: 42巻 Pages: 495101-495101
  • Peer Reviewed
• [Journal Article] The n-level spectral correlations for chaotic systems (2009)
  • Author(s): Taro Nagao and Sebastian Muller
  • Journal Title: J. Phys. A: Math. Theor. Volume: 42巻 Pages: 375102-375102
  • 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: 495101-495101
  • 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: 375102-375102
  • Peer Reviewed
• [Journal Article] The m-level spectrsl correlations for ersctic syscems (2009)
  • Author(s): Taro Nagao, Sebastian Muller
  • Journal Title: J. Phys. A : Math. Theor. 42 Pages: 375102-375102
  • Peer Reviewed
• [Journal Article] Semiclassicel theory for universelity in qusntum cheos with symmetry crossover (2009)
  • Author(s): Keiji Saito, Taro Nagao, sebastian Muller, Petr Brsun
  • Journal Title: J. Phys. A : Math. Thear. 42 Pages: 495101-495101
  • Peer Reviewed
• [Journal Article] Skeworthogonal polynomials and the partly symmetric real Ginibre ensemble (2008)
  • Author(s): Peter J. Forrester and Taro Nagao
  • Journal Title: J. Phys. A: Math. Theor. Volume: 41巻 Pages: 375003-375003
  • 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: 375003-375003
  • Peer Reviewed
• [Journal Article] Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble (2008)
  • Author(s): Peter J. forrester, Taro Nagao
  • Journal Title: J. Phys. A : Math, THeor. 41 Pages: 375003-375003
  • Peer Reviewed
• [Presentation] スケールフリーネットワークのスペクトル密度 III (2013)
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会第68回年次大会
  • Place of Presentation: 広島大学
  • Year and Date: 2013-03-28
• [Presentation] Spectral density of bipartite scale-free networks (2012)
  • Author(s): Taro Nagao
  • 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: 2012-12-05
• [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] 進化するランダム行列理論 (2012)
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会2012年秋季大会 シンポジウム「ランダム行列の過去・現在・未来」
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2012-09-21
• [Presentation] Real asymmetric random matrices and skew orthogonal polynomials on the complex plane (2012)
  • Author(s): Taro Nagao
  • Organizer: International Symposium on Orthogonal Polynomials and Special Functions - a Complex Analytic Perspective
  • Place of Presentation: The Royal Danish Academy of Sciences and Letters
  • Year and Date: 2012-06-12
• [Presentation] スケールフリーネットワークのスペクトル密度 II (2012)
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2012-03-26
• [Presentation] スケールフリーネットワークのスペクトル密度II (2012)
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2012-03-26
• [Presentation] A two-matrix model describing the transition between chiral and non-chiral random matrices (2011)
  • Author(s): Taro Nagao
  • 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: 2011-12-01
• [Presentation] A two-matrix model describing the transition between chiral and non-chiral random matrices (2011)
  • 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(招待講演)
  • Year and Date: 2011-12-01
• [Presentation] スケールフリーネットワークのスペクトル密度 (2011)
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会2011年秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-23
• [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: 慶應義塾大学
  • Year and Date: 2010-12-09
• [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: Spectra of Random Operators and Related Topics
  • Place of Presentation: 京都大学
  • Year and Date: 2009-12-03
• [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] 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] 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ワ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] 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] Eigenvalu 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"Random Tilings, Random Partitions and Stochastic Growth Processes"
  • Place of Presentation: Universite de Montreal
  • Year and Date: 2008-09-03
• [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
• [Presentation] Vicious walks and matrix models (2008)
  • Author(s): Taro Nagao
  • Organizer: Workshop"Randomtilings, random partitions and stochastic growth processes"
  • Place of Presentation: Universite de Montreal
  • Year and Date: 2008-09-03
• [Presentation] Real asymmetric random matrices and skew orthogonal polynomials on the complex plane
  • Author(s): Taro Nagao
  • Organizer: International Symposium on Orthogonal Polynomials and Special Functions - a Complex Analytic Perspective
  • Place of Presentation: The Royal Danish Academy of Sciences and Letters, Copenhagen, Denmark
• [Presentation] 進化するランダム行列理論
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会２０１２年秋季大会
  • Place of Presentation: 横浜国立大学
• [Presentation] Spectral density of bipartite scale-free networks
  • Author(s): Taro Nagao
  • Organizer: Spectra of Random Operators and Related Topics
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] スケールフリーネットワークのスペクトル密度 III
  • Author(s): 永尾太郎
  • Organizer: 日本物理学会第６８回年次大会
  • Place of Presentation: 広島大学
• [Book] The Oxford Handbook of Random Matrix Theory (2011)
  • Author(s): G.J. Rodgers and Taro Nagao
  • Publisher: Oxford University Press
• [Book] The Oxford Handbook of Random Matrix Theory (2011)
  • Author(s): G.J.Rodgers, Taro Nagao
  • Publisher: Oxford University Press