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2012 Fiscal Year Final Research Report

Dynamical Barrier and Quantum localization: Theory of Hamiltonian Dynamics with mixed phase space

Research Project

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Project/Area Number 21540394
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 InstitutionTokyo Metropolitan University

Principal Investigator

SHUDO Akira  首都大学東京, 大学院・理工学研究科, 教授 (60206258)

Co-Investigator(Kenkyū-buntansha) TANAKA Atushi  首都大学東京, 大学院・理工学研究科, 助教 (20323264)
Co-Investigator(Renkei-kenkyūsha) SAITO Shinji  分子科学研究所, 計算科学研究系, 教授 (70262847)
ISHII Yutaka  九州大学, 数理学研究院, 准教授 (20304727)
Project Period (FY) 2009 – 2012
Keywordsカオス / 量子カオス / ハミルトン系 / 非可積分系 / 混合位相空間 / 遅い緩和 / 量子トンネル効果 / 複素力学系 / 半古典論 / 完全WKB解析 / ストークス現象
Research Abstract

Hamiltonian systems with mixed phase space have been studied. The mechanism of slow motionin classical dynamics has been analyzed and the interplay between quantum localizations with different origins has been examined into details.

  • Research Products

    (35 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (11 results) (of which Peer Reviewed: 9 results) Presentation (19 results) Book (4 results) Remarks (1 results)

  • [Journal Article] Tunneling effect and natural boundary of invariant torus2012

    • Author(s)
      A.Shudo and K.S.Ikeda
    • Journal Title

      Phys.Rev.Lett.

      Volume: 109 Pages: 154102 (5)

    • DOI

      doi:10.1103/PhysRevLett.109.154102

    • Peer Reviewed
  • [Journal Article] Flooding of wave functions in multi-dimensional mixed systems and the possibility of experimental observation2012

    • Author(s)
      A. Ishikawa, A. Tanaka, Y. Hanada and A. Shudo
    • Journal Title

      AIP Conference Proceedings

      Volume: Vol. 1468 Pages: 340-349

    • DOI

      doi:http://dx.doi.org/10.1063/1.4745593

  • [Journal Article] Diffraction and tunneling in systems with mixed phase space2012

    • Author(s)
      A.Ishikawa, A.Tanaka, A.Shudo, and K.S.Ikeda
    • Journal Title

      Phys.Rev.E

      Volume: 86 Pages: 136208(14)

    • DOI

      doi:10.1103/PhysRevE.86.036208

    • Peer Reviewed
  • [Journal Article] Weyl law for open systems with sharply divided mixed phase space2012

    • Author(s)
      A.Ishii, A.Akaishi, A.Shudo, and H.Schomerus
    • Journal Title

      Phys.Rev.E

      Volume: 85 Pages: 146203(7)

    • DOI

      doi:10.1103/PhysRevE.85.046203

    • Peer Reviewed
  • [Journal Article] Meeting time distributions in Bernoulli systems2011

    • Author(s)
      A.Akaishi, M.Hirata, K.Yamamoto and A.Shudo
    • Journal Title

      J.Phys.A:Math.Theor

      Volume: 44 Pages: 375101(12)

    • DOI

      doi:10.1088/1751-8113/44/37/375101

    • Peer Reviewed
  • [Journal Article] Boundary element method and isospectrality in quantum billiards2011

    • Author(s)
      T.Harayama and A.Shudo
    • Journal Title

      物性研究

      Volume: 97 Pages: 414-420

  • [Journal Article] Dynamical tunneling in many-dimensional chaotic systems2010

    • Author(s)
      A.Ishikawa, A.Tanaka and A.Shudo
    • Journal Title

      Phys.Rev.Lett.

      Volume: 104 Pages: 224102(4)

    • DOI

      doi:10.1103/PhysRevLett.104.224102

    • Peer Reviewed
  • [Journal Article] ulia set and chaotic tunneling II2009

    • Author(s)
      A.Shudo, Y.Ishii and K.S.Ikeda
    • Journal Title

      J.Phys.A: Math.Theor.

      Volume: 42 Pages: 265102(34)

    • DOI

      doi:10.1088/1751-8113/42/26/265102

    • Peer Reviewed
  • [Journal Article] Recovery of chaotic tunneling due to destruction of dynamical localization by an external noise2009

    • Author(s)
      A.Ishikawa, A.Tanaka and A.Shudo
    • Journal Title

      Phys.Rev.E

      Volume: 80 Pages: 046204(13)

    • DOI

      doi:10.1103/PhysRevE.80.046204

    • Peer Reviewed
  • [Journal Article] Accumulation of unstable periodic orbits and the stickiness in the two-dimensional piecewise linear map2009

    • Author(s)
      A.Akaishi and A.Shudo
    • Journal Title

      Phys.Rev.E

      Volume: 80 Pages: 066211(12)

    • DOI

      doi:10.1103/PhysRevE.80.066211

    • Peer Reviewed
  • [Journal Article] Julia sets and chaotic tunneling I2009

    • Author(s)
      A.Shudo, Y.Ishii, and K.S.Ikeda
    • Journal Title

      J.Phys.A: Math.Theor.

      Volume: 42 Pages: 265101(26)

    • DOI

      doi:10.1088/1751-8113/42/26/265101

    • Peer Reviewed
  • [Presentation] 混合系の量子論と複素力学系におけるエルゴード問題2013

    • Author(s)
      首藤 啓
    • Organizer
      非線形・平衡系シンポジウム- 新しいエルゴード問題の探究-
    • Place of Presentation
      早稲田大学
    • Year and Date
      20130300
  • [Presentation] Introduction to exact WKB method2012

    • Author(s)
      A. Shudo
    • Organizer
      The 11th Christmas symposium of Physicists
    • Place of Presentation
      Maribor, Slovenia
    • Year and Date
      20121200
  • [Presentation] Numerical verification of the exact WKB analysis for multilevel nonadiabatic transition problems2012

    • Author(s)
      R. Ohashi and A. Shudo
    • Organizer
      Recent developments in microlocal analysis and asymptotic analysis
    • Place of Presentation
      RIMS, Kyoto
    • Year and Date
      20121000
  • [Presentation] Tunneling effect and the natural boundary of invariant tori2012

    • Author(s)
      A. Shudo
    • Organizer
      Post Advanced Study Group meeting
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      20121000
  • [Presentation] Role of natural boundaries of KAM curves in quantum tunneling problems2011

    • Author(s)
      A. Shudo
    • Organizer
      Let's face chaos through nonlinear dynamics
    • Place of Presentation
      Maribor, Slovenia
    • Year and Date
      20110700
  • [Presentation] What does theory of complex dynamics tell us ?2011

    • Author(s)
      A. Shudo
    • Organizer
      MPIPKS focus meeting, Dynamical Tunneling in Non-Integrable Systems
    • Place of Presentation
      Dresden, German
    • Year and Date
      20110600
  • [Presentation] Diffraction and Tunneling in the system with sharply divided phase space2011

    • Author(s)
      A. Shudo
    • Organizer
      International workshop on mircrocavities and their applications (WOMA2011)
    • Place of Presentation
      Pusan University, South Korea
    • Year and Date
      20110500
  • [Presentation] Quantum tunneling with and without chaos2011

    • Author(s)
      A. Shudo
    • Organizer
      Satellite meeting of the international workshop on mircrocavities and their applications (WOMA2011)
    • Place of Presentation
      Seoul National University, South Korea
    • Year and Date
      20110500
  • [Presentation] A role of new Stokes curves and virtual turning points in multilevel non-adiabatic transition problems2011

    • Author(s)
      A. Shudo
    • Organizer
      RIMS workshop on Exponential asymptotics and virtual turning points
    • Place of Presentation
      RIMS, Kyoto
    • Year and Date
      20110300
  • [Presentation] 複素力学系と高次元トンネル効果における転移現象2011

    • Author(s)
      首藤 啓
    • Organizer
      第5回ハミルトン力学系セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      20110200
  • [Presentation] 古典および量子カオス2011

    • Author(s)
      首藤 啓
    • Organizer
      早稲田大学物理及応用物理学専攻講演会
    • Place of Presentation
      早稲田大学
    • Year and Date
      20110200
  • [Presentation] Interior and exterior problem in quantum billiards2010

    • Author(s)
      A. Shudo
    • Organizer
      13th Slovenia-Japan International Workshop on Nonlinear Dynamics
    • Place of Presentation
      Waseda
    • Year and Date
      20101100
  • [Presentation] カオス --- 偶然と必然が同居する摩訶不思議な世界2010

    • Author(s)
      首藤 啓
    • Organizer
      高知工科大学特別講義
    • Place of Presentation
      高知工科大学
    • Year and Date
      20100700
  • [Presentation] Julia sets and chaotic tunneling, Tunneling Day2010

    • Author(s)
      A. Shudo
    • Organizer
      Lewiner Institute for Theoretical Physics
    • Place of Presentation
      Haifa, Israel
    • Year and Date
      20100500
  • [Presentation] Pruning theory of Stokes geometry, MPIPKS Workshop2009

    • Author(s)
      A. Shudo
    • Organizer
      Tunneling and Scattering in Complex Systems --- from single to many particle physics---
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      20090900
  • [Presentation] Complex semiclassical approach to chaotic tunneling problem (part III), MPIPKS Workshop2009

    • Author(s)
      A. Shudo
    • Organizer
      Tunneling and Scattering in Complex Systems --- from single to many particle physics---
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      20090900
  • [Presentation] Complex semiclassical approach to chaotic tunneling problem (part II), MPIPKS Workshop2009

    • Author(s)
      A. Shudo
    • Organizer
      Tunneling and Scattering in Complex Systems --- from single to many particle physics---
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      20090900
  • [Presentation] Dynamical localization and dynamical tunneling2009

    • Author(s)
      A. Shudo
    • Organizer
      International workshop on mircrocavities and their applications (WOMA)
    • Place of Presentation
      Seoul National University, South Korea
    • Year and Date
      20090800
  • [Presentation] Role of natural boundaries of KAM curves in dynamical tunneling problems2009

    • Author(s)
      A. Shudo
    • Organizer
      RIMS workshop on New development of asymptotic analysis and dynamical systems
    • Place of Presentation
      RIMS, Kyoto
    • Year and Date
      20090600
  • [Book] 数理物理 私の研究2012

    • Author(s)
      首藤 啓
    • Total Pages
      219-224
    • Publisher
      シュプリンガー
  • [Book] 古典と量子の間2011

    • Author(s)
      首藤 啓
    • Total Pages
      144
    • Publisher
      岩波書店
  • [Book] Complex semiclassical approach to chaotic tunneling in "Dynamical Tunneling" edited by Srihari Keshavamurthy and Peter Schlagheck(Chapter 7)2011

    • Author(s)
      A. Shudo and K. S. Ikeda
    • Total Pages
      139-176
    • Publisher
      CRC Press
  • [Book] 別冊数理科学2010

    • Author(s)
      首藤 啓
    • Total Pages
      181-187
    • Publisher
      サイエンス社
  • [Remarks]

    • URL

      http://www.comp.tmu.ac.jp/nonlinear/ja/index.html

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Published: 2014-08-29   Modified: 2014-09-05  

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