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

Research Project

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
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / カオス的トンネル効果 / 複素半古典論 / 自然境界 / 古典カオス / 動的トンネル効果 / ストークス幾何 / 非断熱遷移 / 動的局在 / カオス的トンネル / アンダーソン転移
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.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (71 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 12 results) Presentation (51 results) (of which Invited: 5 results) Book (5 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 Issue: 15 Pages: 154102-154102

    • DOI

      10.1103/physrevlett.109.154102

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • 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

      10.1063/1.4745593

    • Related Report
      2012 Final Research Report
  • [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 Issue: 3

    • DOI

      10.1103/physreve.86.036208

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • 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 Issue: 4

    • DOI

      10.1103/physreve.85.046203

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • 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 Issue: 37 Pages: 375101-375101

    • DOI

      10.1088/1751-8113/44/37/375101

    • Related Report
      2012 Final Research Report 2011 Annual Research Report 2010 Annual Research Report
    • 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

    • Related Report
      2012 Final Research Report 2011 Annual Research Report 2010 Annual Research Report
  • [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 Issue: 22

    • DOI

      10.1103/physrevlett.104.224102

    • Related Report
      2012 Final Research Report
    • 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 Issue: 26 Pages: 265102-265102

    • DOI

      10.1088/1751-8113/42/26/265102

    • Related Report
      2012 Final Research Report
    • 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 Issue: 4

    • DOI

      10.1103/physreve.80.046204

    • Related Report
      2012 Final Research Report
    • 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 Issue: 6

    • DOI

      10.1103/physreve.80.066211

    • Related Report
      2012 Final Research Report
    • 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 Issue: 26 Pages: 265101-265101

    • DOI

      10.1088/1751-8113/42/26/265101

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Accumulation of unstable periodic orbits and the stickiness in the two-dimensional piecewise linear map2009

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

      Physical Review E 80

      Pages: 66221-66221

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recovery of chaotic tunneling due to destruction of dynamical localization by an external noise2009

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

      Physical Review E 80

      Pages: 46204-46204

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Julia sets and chaotic tunneling I2009

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

      Journal of Physics A 42

      Pages: 265101-265101

    • Related Report
      2009 Annual Research Report
    • 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
    • Related Report
      2012 Final Research Report
  • [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・非平衡系シンポジウム -新しいエルゴード問題の探求-
    • Place of Presentation
      早稲田大学 染谷記念国際会館
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 非可積分系におけるトンネル効果2013

    • Author(s)
      花田康高
    • Organizer
      非線形・非平衡系シンポジウム -新しいエルゴード問題の探求-
    • Place of Presentation
      早稲田大学 染谷記念国際会館
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Semiclassical theory of tunneling splittings and the singularity structure in nonlinear resonances2013

    • Author(s)
      H. Harada and A. Shudo
    • Organizer
      The Global Human Resource Program Bridging across Physics and Chemistry
    • Place of Presentation
      Tokyo Metropolitan University
    • Related Report
      2012 Annual Research Report
  • [Presentation] Wave packet recurrence in strongly chaotic systems2013

    • Author(s)
      Y. Hanada, Y. Sugiyama and A. Shudo
    • Organizer
      The Global Human Resource Program Bridging across Physics and Chemistry
    • Place of Presentation
      Tokyo Metropolitan University
    • Related Report
      2012 Annual Research Report
  • [Presentation] 不安定周期軌道と混合位相空間をもつカオス系のトンネル分裂について2013

    • Author(s)
      花田康高,首藤啓
    • Organizer
      日本物理学会 2012年度 春季大会
    • Place of Presentation
      広島大学,東広島キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] 離散時間系におけるエネルギー分裂の半古典論について2013

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会 2012年度 春季大会
    • Place of Presentation
      広島大学,東広島キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] 区分線型写像における階層構造の複雑さ2013

    • Author(s)
      青木和輝, 赤石暁, 首藤啓
    • Organizer
      日本物理学会 2012年度 春季大会
    • Place of Presentation
      広島大学,東広島キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] Complex paths for regular-to-chaotic tunneling rates2012

    • Author(s)
      A.Backer, R.Ketzmerick, S.Lock, N.Mertig, A.Shudo
    • Organizer
      Annual spring meeting of the German Physical Society
    • Place of Presentation
      Berlin
    • Year and Date
      2012-03-23
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] Flooding of tunneling flux in the Kepler map2012

    • Author(s)
      Y.Hanada, K.S.Ikeda, A.Shudo
    • Organizer
      Dynamics days 2012
    • Place of Presentation
      Univ.of Maryland
    • Year and Date
      2012-01-04
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] Meeting time distributions in dynamical systems2012

    • Author(s)
      A.Akaishi, M.Hirata, K.Yamamoto, A.Shudo
    • Organizer
      Dynamics days 2012
    • Place of Presentation
      Univ.of Maryland
    • Year and Date
      2012-01-04
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] Introduction to exact WKB method2012

    • Author(s)
      A. Shudo
    • Organizer
      The 11th Christmas symposium of Physicists
    • Place of Presentation
      Maribor, Slovenia
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [Presentation] 完全WKB解析による3準位の非断熱遷移について2012

    • Author(s)
      大橋るり子,金井真澄,首藤啓
    • Organizer
      日本物理学会 2012年秋季大会
    • Place of Presentation
      横浜国立大学 常盤台キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] エネルギー分裂に関する半古典論と複素古典軌道のトポロジー2012

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会 2012年秋季大会
    • Place of Presentation
      横浜国立大学 常盤台キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] 複素ポテンシャルを用いた量子開放系の解析2012

    • Author(s)
      花田康高,首藤啓
    • Organizer
      日本物理学会 2012年秋季大会
    • Place of Presentation
      横浜国立大学 常盤台キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] Sharply-divided Phase Spaceのベキ則2012

    • Author(s)
      赤石暁,首藤啓
    • Organizer
      日本物理学会 2012年秋季大会
    • Place of Presentation
      横浜国立大学 常盤台キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] Numerical verification of the exact WKB analysis for multilevel nonadiabatic transition problems2012

    • Author(s)
      R. Ohashi and A. Shudo
    • Organizer
      RIMS研究集会「超局所解析と漸近解析の最近の進展」
    • Place of Presentation
      京都大学 数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Tunneling effect and the natural boundary of invariant tori2012

    • Author(s)
      A. Shudo
    • Organizer
      Post advanced study group meeting
    • Place of Presentation
      Max Planck Institute for Physics of Complex Systems, Dresden (Germany)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Wave packet recurrence in strongly chaotic systems2012

    • Author(s)
      Y. Hanada, Y. Sugiyama and A. Shudo
    • Organizer
      Workshop of Quantum Dynamics and Quantum Walks
    • Place of Presentation
      Institute for Molecular Science
    • Related Report
      2012 Annual Research Report
  • [Presentation] An introduction to exact WKB method2012

    • Author(s)
      A. Shudo
    • Organizer
      The 11th Christmas symposium of Physicists
    • Place of Presentation
      Maribor(Slovenia)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Flooding of tunneling flux in the Kepler map2011

    • Author(s)
      Y.Hanada, K.S.Ikeda, A.Shudo
    • Organizer
      International Symposium on Nano Science and Functional Materials : Post-symposium of International Symposium on Catalysis and Fine Chemicals 2011
    • Place of Presentation
      Tokyo Metropolitan Univ.
    • Year and Date
      2011-12-01
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] カオス的トンネル効果の複素半古典論2011

    • Author(s)
      池田研介, 首藤啓
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Year and Date
      2011-09-24
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] ケプラー写像におけるカオス的トンネル効果の異常増大2011

    • Author(s)
      花田康高, 首藤啓, 池田研介
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Year and Date
      2011-09-24
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] トンネル複素軌道と部分wick回転2011

    • Author(s)
      原田浩充, 首藤啓
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Year and Date
      2011-09-24
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] 混合位相空間におけるmeeting timeの分布2011

    • Author(s)
      赤石暁, 平田雅樹, 山本謙一郎, 首藤啓
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Year and Date
      2011-09-22
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] Role of natural boundaries of KAM curves in quantum tunneling problems2011

    • Author(s)
      A.Shudo
    • Organizer
      International Summer School/Conference "Let's face chaos through nonlinear dynamics"
    • Place of Presentation
      Maribor, Slovenia
    • Year and Date
      2011-07-07
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [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
      Max Planck Institute (Dresden)
    • Year and Date
      2011-06-14
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [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 national univ.
    • Year and Date
      2011-05-24
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Presentation] Quantum tunneling with and without chaos2011

    • Author(s)
      A.Shudo
    • Organizer
      Satellite meeting of the international workshop on mirc rocavities and their applications
    • Place of Presentation
      Seoul national univ.
    • Year and Date
      2011-05-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Quantum tunneling with and without chaos2011

    • Author(s)
      A.Shudo
    • Organizer
      Satellite meeting of the international workshop on mircrocavities and their applications
    • Place of Presentation
      Seoul national univ.
    • Year and Date
      2011-05-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] 力学系のmeeting timeの分布III2011

    • Author(s)
      赤石暁, 平田雅樹, 山本謙一郎, 首藤啓
    • Organizer
      日本物理学会第66回年次大会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] ケプラー写像における動的トンネル確率の異常増大2011

    • Author(s)
      花田康高, 首藤啓, 池田研介
    • Organizer
      日本物理学会第66回年次大会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] 多準位の非断熱遷移とストークス幾何2011

    • Author(s)
      金井真澄, 首藤啓
    • Organizer
      日本物理学会第66回年次大会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-25
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [Presentation] Julia sets and chaotic tunneling, Tunneling Day2010

    • Author(s)
      A. Shudo
    • Organizer
      Lewiner Institute for Theoretical Physics
    • Place of Presentation
      Haifa, Israel
    • Related Report
      2012 Final Research Report
  • [Presentation] Dynamical localization and dynamical tunneling2009

    • Author(s)
      A.Shudo
    • Organizer
      International workshop on mircrocavities and their applications
    • Place of Presentation
      Soul National University
    • Year and Date
      2009-08-24
    • Related Report
      2009 Annual Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [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
    • Related Report
      2012 Final Research Report
  • [Book] 数理物理 私の研究2012

    • Author(s)
      首藤 啓
    • Publisher
      シュプリンガー
    • Related Report
      2012 Final Research Report
  • [Book] 数理物理 私の研究 (シュプリンガー量子数理シリーズ)2012

    • Author(s)
      首藤 啓
    • Total Pages
      6
    • Publisher
      シュプリンガー
    • Related Report
      2012 Annual Research Report
  • [Book] 古典と量子の間2011

    • Author(s)
      首藤 啓
    • Total Pages
      144
    • Publisher
      岩波書店
    • Related Report
      2012 Final Research Report
  • [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
    • Publisher
      CRC Press
    • Related Report
      2012 Final Research Report
  • [Book] 別冊数理科学2010

    • Author(s)
      首藤 啓
    • Publisher
      サイエンス社
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2012 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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