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The fundamental problem of classical dynamics'' in the complexified space and non-integrable tunneling phenomena

Research Project

Project/Area Number 15H03701
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

IKEDA Kensuke  立命館大学, 理工学部, 教授 (40151287)

Co-Investigator(Kenkyū-buntansha) 首藤 啓  首都大学東京, 理工学研究科, 教授 (60206258)
高橋 公也  九州工業大学, 大学院情報工学研究院, 教授 (70188001)
Research Collaborator YAMADA Hiroaki  山田物理学研究所
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000)
Fiscal Year 2017: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Keywordstunneling effect / semiclassical theory / nonintegrable sysem / quantum chaos / dynamical theory / nonintegrable system
Outline of Final Research Achievements

First, the transition process from the instanton tunneling, the typical tunneling process in integrable system, to the non-instanton (NI) tunneling process is elucidated by developing a renormalized perturbation method. The remarkable characteristics of the NI tunneling process is clearly explained as an unrenormalizable action of the resonant interaction. Next, the Stokes geometry, which provide rich information for solving an essential difficulty interent in our complexified semiclassical method, is clarified for a quantum map system in the ideally chaotic regime (the so-called horseshoe limit). Finally, a new method for investigating quantum chaotic mixing from  the auto-correlation characteristics is proposed, and the lifetime in which classical chaotic mixing is maintained in the quantum counterpart is shown to be much longer than the one which has been conjectured so far.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (60 results)

All 2018 2017 2016 2015

All Journal Article (11 results) (of which Peer Reviewed: 11 results,  Acknowledgement Compliant: 3 results) Presentation (47 results) (of which Int'l Joint Research: 12 results,  Invited: 12 results) Book (1 results) Funded Workshop (1 results)

  • [Journal Article] Scaling properties of dynamical localization in monochromatically perturbed quantum maps:Standard map and Anderson map2018

    • Author(s)
      Hiroaki S.Yamada, Fumihiro Matsui, and Kensuke S.Ikeda
    • Journal Title

      Phys. Rev. E

      Volume: 97 Pages: 0122101-13

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hierarchical structure in sharply divided phase space for the piecewise linear map2017

    • Author(s)
      Akaishi, Akira and Aoki, Kazuki and Shudo, Akira
    • Journal Title

      Phys. Rev. E

      Volume: 95 Issue: 5 Pages: 0522071-8

    • DOI

      10.1103/physreve.95.052207

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems2017

    • Author(s)
      Hiromitsu Harada, Amaury Mouchet and Akira Shudo
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 30 Issue: 43 Pages: 435204-435204

    • DOI

      10.1088/1751-8121/aa8c67

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relation between irreversibility and entanglement in classically chaotic quantum kicked rotors2016

    • Author(s)
      F.Matsui, H.S.Yamada and K.S.Ikeda
    • Journal Title

      Europhys. Lett.

      Volume: 114 Issue: 6 Pages: 1-5

    • DOI

      10.1209/0295-5075/114/60010

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toward pruning theory for the Stokes geometry of the quantum Henon map2016

    • Author(s)
      Akira Shudo and Kensuke S. Ikeda
    • Journal Title

      Nonlinearity

      Volume: 29 Issue: 2 Pages: 375-425

    • DOI

      10.1088/0951-7715/29/2/375

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] "Measuring lifetime of correspondence with classical decay of cor-relation in quantum chaos"2016

    • Author(s)
      Fumihiro Matsui, Hiroaki S.Yamada and Kensuke S.Ikeda
    • Journal Title

      Euro Phys. Lett.

      Volume: -

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Origin of the enhancement of tunneling probability in the nearly integrable system2015

    • Author(s)
      Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda
    • Journal Title

      Physical Review E

      Volume: 91 Issue: 4 Pages: 0429131-16

    • DOI

      10.1103/physreve.91.042913

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Critical Phenomena of Dynamical Delocalization in Quantum Anderson Map2015

    • Author(s)
      Hiroaki S.Yamada, Fumihiro Matsui, and Kensuke S. Ikeda
    • Journal Title

      Physical Review E

      Volume: 92 Issue: 6

    • DOI

      10.1103/physreve.92.062908

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical verification of the exact WKB formula for the generalized Landau-Zener-Stueckelberg problem,2015

    • Author(s)
      Akira Shudo and Ruriko Ohashi
    • Journal Title

      Advances in Science, Technology and Environmentology, Special issue : ASTE (Waseda University)

      Volume: B11 Pages: 75-80

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Resonance-assisted tunneling in integrable and nonintegrable systems,2015

    • Author(s)
      Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda
    • Journal Title

      Advances in Science, Technology and Environmentology, Special issue : ASTE (Waseda University)

      Volume: B11 Pages: 127-130

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-linear resonances and singularity structures of complex classical dynamics,2015

    • Author(s)
      Hiromitsu Harada and Akira Shudo
    • Journal Title

      Advances in Science, Technology and Environmentology, Special issue : ASTE (Waseda University)

      Volume: B11 Pages: 131-134

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Presentation] 馬蹄条件下での半古典近似の長時間有効性について2018

    • Author(s)
      吉野元,首藤啓
    • Organizer
      日本物理学会(第73回年次大会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 完全WKB解析とストークス幾何に基づく三準位非断熱遷移問題の研究2018

    • Author(s)
      島田尚明,首藤啓
    • Organizer
      日本物理学会(第73回年次大会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 非カオス的な面積保存写像における劣拡散を記述する確率モデルについて2018

    • Author(s)
      吉田賢典,渡邉真悟,首藤啓
    • Organizer
      日本物理学会(第73回年次大会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 対応原理によるインスタントン 非インスタントン転移の研究III2017

    • Author(s)
      池田研介,花田康高,首藤啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市豊中キャンパス)
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 複素古典軌道のリーマン面と可積分系のトンネル分裂2017

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市豊中キャンパス)
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 可積分写像におけるトンネル異常2017

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市豊中キャンパス)
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 劣拡散を示す非カオス的な区分線型面積保存写像における待ち時間分布と連続時間ランダムウォーク2017

    • Author(s)
      吉田 賢典,渡邉 真悟,首藤 啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市豊中キャンパス)
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] カオス系における時間領域半古典近似の破綻するタイムスケールについて2017

    • Author(s)
      吉野 元,首藤 啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市豊中キャンパス)
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Infinitely many stability islands and sticky dynamics in a piecewise linear map2017

    • Author(s)
      Akira Shudo
    • Organizer
      The 6th Hamiltonian dynamical systems and related topics
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2017-03-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum tunneling in the classically chaotic systems2017

    • Author(s)
      Yasutaka Hanada
    • Organizer
      Workshop on Chaos and Diffusion in Leaky Systems
    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Year and Date
      2017-02-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 対応原理によるインスタントン 非インスタントン転移の研究 IV2017

    • Author(s)
      池田研介, 花田康高, 首藤啓
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 単色摂動アンダーソン写像および標準写像の2次元局在現象2017

    • Author(s)
      池田研介, 山田弘明
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 量子写像のBaker-Campbell-Hausdorff展開について2017

    • Author(s)
      花田康高, 首藤啓, 池田研介
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 馬蹄条件を満たすカオス系における半古典近似破綻領域の漸近挙動2017

    • Author(s)
      吉野元,首藤啓
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 劣拡散を示す面積保存写像における周期軌道近傍の淀み運動と連続時間ランダムウォーク2017

    • Author(s)
      吉田賢典,渡邉真悟,首藤啓
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Amphibious Complex Orbits and Dynamical Tunneling2017

    • Author(s)
      Akira Shudo
    • Organizer
      “Chaos, and what it can reveal” A conference on the occasion of Petr Seba's 60th birthday
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Sub-diffusion in a non-chaotic area-preserving map, continuous-time random walks and ergodic problems2017

    • Author(s)
      Kensuke Yoshida, Shingo Watanabe, Akira Shudo
    • Organizer
      Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen
    • Related Report
      2017 Annual Research Report
  • [Presentation] A Quantum Damper2017

    • Author(s)
      池田研介
    • Organizer
      第24回「レーザーのカオス・ノイズダイナミックスとその応用」研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 量子カオス系における固有状態の重ね合わせと不可逆性の寿命2016

    • Author(s)
      松井文宏, 山田弘明, 池田研介
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 対応原理によるインスタントン 非インスタントン移の研究2016

    • Author(s)
      池田研介, 奥島輝昭, 花田康高, 首藤啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 対応原理によるインスタントン 非インスタントン移の研究II2016

    • Author(s)
      池田研介, 奥島輝昭, 花田康高, 首藤啓
    • Organizer
      日本物理学会 第72回年次大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 非可積分系のトンネル効果と古典共鳴の役割について2016

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 2016年秋季大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 区分線型面積保存写像における劣拡散と連続時間ランダムウォーク2016

    • Author(s)
      吉田 賢典,渡邉 真悟,首藤 啓
    • Organizer
      日本物理学会 2016年秋季大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-13
    • Related Report
      2016 Annual Research Report
  • [Presentation] Toward pruning theory for the Stokes geometry of the quantum Henon map2016

    • Author(s)
      Akira Shudo
    • Organizer
      Quantum Chaos, Graphs and Nodal Domains
    • Place of Presentation
      Weizmann Institute (Rehovot, Israel)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Amphibious Complex Orbits and Dynamical Tunneling2016

    • Author(s)
      Akira Shudo
    • Organizer
      PHHQP16: Progress in Quantum Physics with Non-Hermitian Operator
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-08-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tunneling in nearly integrable systems with a non-hermitian perturbation2016

    • Author(s)
      Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda
    • Organizer
      PHHQP16: Progress in Quantum Physics with Non-Hermitian Operator
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-08-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Toward pruning theory for the Stokes geometry of the quantum Henon map2016

    • Author(s)
      Akira Shudo
    • Organizer
      数理解析研究所研究会 『力学系とその関連分野の連携探索』
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-06-06
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Anomalous behavior of transition matrix elements in nonintegrable quantum maps2016

    • Author(s)
      Akira Shudo
    • Organizer
      RIMS workshop “Exponential Asymptotics of Difference and Differential Equations”
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-06-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 非可積分系におけるトンネル分裂の階段構造について II2016

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 第71回年次大会
    • Place of Presentation
      東北学院大学(宮城県仙台市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] 古典系における動的局在と区分線型面積保存写像における軌道の異常拡散について2016

    • Author(s)
      吉田 賢典,渡邉 真悟,首藤 啓
    • Organizer
      日本物理学会 第71回年次大会
    • Place of Presentation
      東北学院大学(宮城県仙台市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] 標準型ハミルトン系のトンネル分裂と複素古典軌道のトポロジー2016

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会 第71回年次大会
    • Place of Presentation
      東北学院大学(宮城県仙台市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] 多自由度ハミルトン系における周期軌道の軌道不安定性に基づく緩和現象の研究 VII2016

    • Author(s)
      奥島輝昭, 池田研介
    • Organizer
      日本物理学会 第71回年次大会
    • Place of Presentation
      東北学院大学(宮城県仙台市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] Exact solution of one-dimensional normal form Hamiltonian system2016

    • Author(s)
      Hiromitsu Harada, Akira Shudo
    • Organizer
      The Global Human Resource Program Bridging across Physics and Chemistry
    • Place of Presentation
      Tokyo Metropolitan University(Hachioji, Tokyo)
    • Year and Date
      2016-01-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Semiclassical analysis of dynamical Anderson localization in chaotic systems2016

    • Author(s)
      Kensuke Yoshida, Akira Shudo
    • Organizer
      The Global Human Resource Program Bridging across Physics and Chemistry
    • Place of Presentation
      Tokyo Metropolitan University(Hachioji, Tokyo)
    • Year and Date
      2016-01-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Quantum mechanics in open systems2016

    • Author(s)
      Hajime Yoshino, Yasutaka Hanada, Akira Shudo
    • Organizer
      The Global Human Resource Program Bridging across Physics and Chemistry
    • Place of Presentation
      Tokyo Metropolitan University(Hachioji, Tokyo)
    • Year and Date
      2016-01-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The existence of infinitely many stability islands and sticky dynamics in a piecewise linear map2015

    • Author(s)
      A. Shudo
    • Organizer
      The 14th Christmas symposium of Physicists
    • Place of Presentation
      Maribor(Slovenia)
    • Year and Date
      2015-12-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 非可積分系のトンネル効果2015

    • Author(s)
      首藤 啓
    • Organizer
      数学協働プログラム、平成27年度ワークショップ 『大自由度分子系における化学反応機序の理解と制御』
    • Place of Presentation
      北海道大学(北海道札幌市)
    • Year and Date
      2015-11-30
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 非可積分系におけるトンネル分裂の階段構造について2015

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 量子系における時間の矢の寿命測定2015

    • Author(s)
      松井文宏, 池田研介, 山田弘明
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 近可積分領域におけるトンネル階段構造とその性質2015

    • Author(s)
      大屋俊弘, 高橋公也, 池田研介
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] インスタントン-非インスタントン転移の実半古典論2015

    • Author(s)
      池田研介, 花田康高, 首藤啓
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] もつれ合いの異常ゆらぎと時間の矢2015

    • Author(s)
      松井文宏, 池田研介, 山田弘明
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 強いカオス系における古典軌道間の相関と波動関数の干渉2015

    • Author(s)
      吉田 賢典,首藤 啓
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 標準型ハミルトン系の古典力学とトンネル分裂2015

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会 2015年秋季大会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] The existence of infinitely many stability islands and sticky dynamics in a piecewise linear map2015

    • Author(s)
      A. Shudo
    • Organizer
      International Workshop on Ray & Wave Mechanics in 2D Microcavity and Related Systems
    • Place of Presentation
      Seoul(Korea)
    • Year and Date
      2015-07-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum tunneling in nonintegrable systems: beyond the leading order semiclassical description2015

    • Author(s)
      首藤 啓
    • Organizer
      数理解析研究所研究会 『計算機を援用した完全WKB解析の研究 ---仮想的変わり点の周辺を中心として ---』
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2015-06-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Nonadiabatic transition in multilevels and the exact WKB method2015

    • Author(s)
      A. Shudo
    • Organizer
      Dynamics Days Central Asia
    • Place of Presentation
      Khiva(Uzbekistan)
    • Year and Date
      2015-05-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] 数理科学2016

    • Author(s)
      首藤 啓
    • Total Pages
      10
    • Publisher
      サイエンス社
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Workshop on Chaos and Diffusion in Leaky Systems2017

    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Year and Date
      2017-02-21
    • Related Report
      2016 Annual Research Report

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Published: 2015-04-16   Modified: 2019-03-29  

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