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2012 Fiscal Year Final Research Report

Universality of Random Matrices and Semiclassical Quantum Theory

Research Project

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Project/Area Number 20540372
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionNagoya 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
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

    (23 results)

All 2013 2012 2011 2010 2009 2008

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (13 results) Book (1 results)

  • [Journal Article] Spectral density of complex networks with two species of nodes2013

    • Author(s)
      Taro Nagao
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 46巻 Pages: 065003

    • Peer Reviewed
  • [Journal Article] Parametric correlations versus fidelity decay: the symmetry breaking case2011

    • Author(s)
      Heiner Kohler, Taro Nagao and Hans-Jurgen Stockmann
    • Journal Title

      Phys. Rev. E

      Volume: 84巻 Pages: 061133

    • Peer Reviewed
  • [Journal Article] Random matrix theory for the Hermitian Wilson Dirac operator and the chGUE-GUE transition2011

    • Author(s)
      Gernot Akemann and Taro Nagao
    • Journal Title

      J. High Energy Phys.

      Volume: 2011巻 Pages: 60

    • Peer Reviewed
  • [Journal Article] Determinantal correlations for classical projection processes2011

    • Author(s)
      Peter J. Forrester and Taro Nagao
    • Journal Title

      J. Stat. Mech.

      Volume: 2011巻 Pages: P08011

    • Peer Reviewed
  • [Journal Article] Spectral correlation functions for chaotic systems2011

    • 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

    • Peer Reviewed
  • [Journal Article] Chaotic transport in the symmetry crossover regime with a spin-orbit interaction2010

    • Author(s)
      Keiji Saito and Taro Nagao
    • Journal Title

      Phys. Rev. B

      Volume: 82巻 Pages: 125322

    • Peer Reviewed
  • [Journal Article] Semiclassical theory for universality in quantum chaos with symmetry crossover2009

    • Author(s)
      Keiji Saito, Taro Nagao, Sebastian Muller and Petr Braun
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 42巻 Pages: 495101

    • Peer Reviewed
  • [Journal Article] The n-level spectral correlations for chaotic systems2009

    • Author(s)
      Taro Nagao and Sebastian Muller
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 42巻 Pages: 375102

    • Peer Reviewed
  • [Journal Article] Skeworthogonal polynomials and the partly symmetric real Ginibre ensemble2008

    • Author(s)
      Peter J. Forrester and Taro Nagao
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 41巻 Pages: 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 III2013

    • 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 networks2012

    • 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 plane2012

    • 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 II2012

    • 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 matrices2011

    • 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] 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] Determinantal spectral correlations for chaotic systems2009

    • 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] Spectral density of the adjacency matrices of complex networks2008

    • 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 ensemble2008

    • 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 models2008

    • 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
  • [Book] The Oxford Handbook of Random Matrix Theory2011

    • Author(s)
      G.J. Rodgers and Taro Nagao
    • Total Pages
      898-911
    • Publisher
      Oxford University Press

URL: 

Published: 2014-08-29  

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