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``The fundamental ploblem of mechanics'' and many-dimensional tunneling

Research Project

Project/Area Number 24340094
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
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) TAKAHASHI Kinya  九州工業大学大学院, 情報工学研究院, 教授 (70188001)
SHUDO Akira  首都大学東京, 理工学研究科, 教授 (60206258)
Research Collaborator KETZMERICK R.  Dresden工大, 理論物理教室, 教授
MOUCHET A.  Francois Rabelais de Tours大学, 数物教室, 講師
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2014: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2013: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2012: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Keywordsカオス / 量子力学 / トンネル効果 / 半古典理論 / 複素力学系 / 非可積分系 / トンネル現象 / 物性基礎論
Outline of Final Research Achievements

The nonintegrability, which was stressed by Poincare as ``the fundamental problem of classical mechanics'', is most sensitively detected by remarkable changes in quantum tunneling process, by distorting the complex phase space. Various phases of the paradoxical assertion are investigated.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (35 results)

All 2015 2014 2013 2012 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results,  Acknowledgement Compliant: 3 results,  Open Access: 2 results) Presentation (25 results) (of which Invited: 6 results)

  • [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

      Phys. Rev.

      Volume: E91 Pages: 0429131-16

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A Numerical Test of Pade Approximation for Some Functions with Singularity2014

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

      International Journal of Computational Mathematics

      Volume: Article ID 587430 Pages: 1-17

    • DOI

      10.1155/2014/587430

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Chaos in Jahn-Teller Rattling2014

    • Author(s)
      Takashi Hotta and Akira Shudo
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 83 Issue: 8 Pages: 087051-5

    • DOI

      10.7566/jpsj.83.083705

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Analyticity of Quantum States in One-Dimensional Tight-Binding Model2014

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

      Euro. Phys. Jour. B

      Volume: 1

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complex paths for regular-to-chaotic tunneling rates2013

    • Author(s)
      N. Mertig, S. Lock, A. Backer, R. Ketzmerick, A. Shudo
    • Journal Title

      Europhys. Lett.

      Volume: 102 Issue: 1 Pages: 10005-10005

    • DOI

      10.1209/0295-5075/102/10005

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] パデ解析による波動関数の特異性診断 その壱2013

    • Author(s)
      山田弘明、池田研介
    • Journal Title

      物性研究電子版

      Volume: 2

    • NAID

      120005312157

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] パデ解析による波動関数の特異性診断 その弐2013

    • Author(s)
      山田弘明、池田研介
    • Journal Title

      物性研究電子版

      Volume: 2

    • NAID

      120005312156

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [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
    • Peer Reviewed
  • [Journal Article] Instanton and noninstanton tunneling in periodically perturbed barriers : Semiclassical and quantum interpretations2012

    • Author(s)
      K. Takahashi, K. S. Ikeda
    • Journal Title

      Phys. Rev.

      Volume: E86 Issue: 5

    • DOI

      10.1103/physreve.86.056206

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [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
    • Peer Reviewed
  • [Presentation] 繰り込み摂動論によるインスタントン 非インスタントン転移の研究III2015

    • Author(s)
      池田研介,奥島輝昭,花田康隆,首藤啓
    • Organizer
      日本物理学会春季大会
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2015-03-21
    • Related Report
      2014 Annual Research Report
  • [Presentation] Quantum tunneling in nonintegrable systems: beyond the leading order semiclassical description2015

    • Author(s)
      A. Shudo
    • Organizer
      Quantum chaos: fundamentals and applications
    • Place of Presentation
      Luchon (France)
    • Year and Date
      2015-03-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Complex dynamics in normal form Hamiltonian systems2015

    • Author(s)
      Hiromitsu Harada, Akira Shudo, Amaury Mouchet, and Jeremy Le Deunff
    • Organizer
      Quantum chaos: fundamentals and applications
    • Place of Presentation
      Luchon (France)
    • Year and Date
      2015-03-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] Staircase-structure in the tunneling splitting curve2015

    • Author(s)
      Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda
    • Organizer
      Quantum chaos: fundamentals and applications
    • Place of Presentation
      Luchon (France)
    • Year and Date
      2015-03-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] an Introduction to the exact WKB analysis2014

    • Author(s)
      A. Shudo
    • Organizer
      Waseda AICS Symposium and the 14th Slovenia-Japan Seminar: New Challenges in Complex Systems Science
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2014-10-25
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Non-linear resonances and singularity structures of complex classical dynamics2014

    • Author(s)
      Hiromitsu Harada, Akira Shudo
    • Organizer
      Waseda AICS Symposium and the 14th Slovenia-Japan Seminar: New Challenges in Complex Systems Science
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2014-10-24 – 2014-10-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] Resonance-assisted tunneling in integrable and nonintegrable systems2014

    • Author(s)
      Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda
    • Organizer
      Waseda AICS Symposium and the 14th Slovenia-Japan Seminar: New Challenges in Complex Systems Science
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2014-10-24 – 2014-10-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] Quantum tunneling in nonintegrable systems: beyond the leading order WKB description Several aspects of microlocal analysis2014

    • Author(s)
      A. Shudo
    • Organizer
      Several aspects of microlocal analysis
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2014-10-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 繰り込み摂動論によるインスタントン 非インスタントン転移の研究2014

    • Author(s)
      池田研介,奥島輝昭,花田康隆,首藤啓
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学(愛知県)
    • Year and Date
      2014-09-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 繰り込み摂動論によるインスタントン 非インスタントン転移の研究II2014

    • Author(s)
      池田研介,奥島輝昭,花田康隆,首藤啓
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学春日井キャンパス(愛知県)
    • Year and Date
      2014-09-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 受動型量子カオス拡散の臨界現象2014

    • Author(s)
      池田研介,松井文宏,山田弘明
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学春日井キャンパス(愛知県)
    • Year and Date
      2014-09-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非可積分系のトンネル効果と複素KAMトーラスの自然境界2014

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学春日井キャンパス(愛知県)
    • Year and Date
      2014-09-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 複素軌道の特異点構造と非線形共鳴2014

    • Author(s)
      原田浩充,首藤啓
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学(愛知県)
    • Year and Date
      2014-09-10
    • Related Report
      2014 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 VI2014

    • Author(s)
      奥島輝昭, 池田研介
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      中部大学(愛知県)
    • Year and Date
      2014-09-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] 区分線型写像の階層構造と再帰軌道の関係2014

    • Author(s)
      青木和輝,赤石暁,首藤啓
    • Organizer
      日本物理学会
    • Place of Presentation
      中部大学(愛知県)
    • Year and Date
      2014-09-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] ハミルトン系における遅い緩和現象について2014

    • Author(s)
      首藤 啓
    • Organizer
      ソフトな物理工学の未来を考える会
    • Place of Presentation
      湘南国際村(神奈川県)
    • Year and Date
      2014-07-12
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Renormalized perturbative analysis of mixed quantum systems and dynamically induced diffraction2014

    • Author(s)
      A. Shudo
    • Organizer
      9th international summer school and conference "Let's face chaos through nonlinear dynamics
    • Place of Presentation
      Maribor(Slovenia)
    • Year and Date
      2014-06-30 – 2014-07-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] KAM曲線の自然境界と動的回折効果について2014

    • Author(s)
      首藤 啓
    • Organizer
      「第5回ハミルトン系とその周辺(伊藤秀一先生還暦記念研究集会)」
    • Place of Presentation
      金沢大学(石川県)
    • Year and Date
      2014-05-29
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 近可積分領域における非インスタントン的トンネル効果

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス(徳島県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 少数自由度量子系における非可逆的エネルギー輸送のモデル

    • Author(s)
      松井文宏, 山田 弘明, 池田 研介
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス(徳島県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 連続時間系トンネル共鳴状態へのカオスの影響とその諸問題

    • Author(s)
      大屋俊弘, 高橋公也, 池田 研介
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス(徳島県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 一次元三重井戸型ポテンシャル系のエネルギー分裂の半古典論

    • Author(s)
      原田浩充,首藤啓,齋藤暁
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス(神奈川県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 近可積分領域における非インスタントン的トンネル効果2

    • Author(s)
      花田康高,首藤啓,池田研介
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス(神奈川県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 量子アーノルド拡散に於ける転移様現象

    • Author(s)
      打田旭宏、松井文宏、池田研介
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス(神奈川県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] インスタントン非インスタントン転移と繰り込み摂動論

    • Author(s)
      池田研介、首藤啓
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス(神奈川県)
    • Related Report
      2013 Annual Research Report

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Published: 2012-04-24   Modified: 2019-07-29  

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