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Generalization of Lyapunov exponent and its application to non-equilibrium non-stationary phenomena

Research Project

Project/Area Number 22740262
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionKeio University

Principal Investigator

AKIMOTO Takuma  慶應義塾大学, 理工学研究科, 特任講師 (30454044)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords数理物理 / 統計力学 / エルゴード理論 / エイジング
Research Abstract

As is well known, a particle found in pollen grains moves irregularly on the surface of water. For such diffusion, the mean square displacement of a particle increases linearly in time and the diffusivity is characterized by its slope, i.e., diffusion con

Report

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

    (33 results)

All 2013 2012 2011 2010 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (21 results) Remarks (2 results)

  • [Journal Article] Aging generates regular motions in weakly chaotic systems2013

    • Author(s)
      T. Akimoto and E. Barkai
    • Journal Title

      Phys. Rev.

      Volume: E 87 Issue: 3

    • DOI

      10.1103/physreve.87.032915

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ergodic properties of continuous-time random walks: Finite-size effects and ensemble dependencies2013

    • Author(s)
      T. Miyaguchi and T. Akimoto
    • Journal Title

      Phys. Rev.

      Volume: E 87 Issue: 3 Pages: 32130-32130

    • DOI

      10.1103/physreve.87.032130

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Distributional response to biases in deterministic superdiffusion2012

    • Author(s)
      T. Akimoto
    • Journal Title

      Phys. Rev. Lett.

      Volume: 108 Issue: 16

    • DOI

      10.1103/physrevlett.108.164101

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalization of the Einstein relation for single trajectories in deterministic subdiffusion2012

    • Author(s)
      T. Akimoto
    • Journal Title

      Phys. Rev.

      Volume: E 85 Issue: 2

    • DOI

      10.1103/physreve.85.021110

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ultraslow Convergence to Ergodicity in Transient Subdiffusion2011

    • Author(s)
      T. Miyaguchi and T. Akimoto
    • Journal Title

      Phys. Rev.

      Volume: E 83 Issue: 6

    • DOI

      10.1103/physreve.83.062101

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Intrinsic Randomness of Transport Coefficient in Subdiffusion with Static Disorder2011

    • Author(s)
      T. Miyaguchi and T. Akimoto
    • Journal Title

      Phys. Rev.

      Volume: E 83 Issue: 3

    • DOI

      10.1103/physreve.83.031926

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Role of infinite invariant measure in deterministic subdiffusion2011

    • Author(s)
      Takuma Akimoto, Tomoshige Miyaguchi
    • Journal Title

      Phys.Rev.E

      Volume: 82

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Intrinsic Randomness of Transport Coefficient in Subdiffusion with Static Disorder2011

    • Author(s)
      Tomoshige Miyaguchi, Takuma Akimoto
    • Journal Title

      Phys.Rev.E

      Volume: 83

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Role of infinite invariant measure in deterministic subdiffusion2010

    • Author(s)
      T. Akimoto and T. Miyaguchi
    • Journal Title

      Phys. Rev.

      Volume: E 82 Issue: 3

    • DOI

      10.1103/physreve.82.030102

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Subexponential instability in one-dimensional maps implies infinite invariant measure2010

    • Author(s)
      Takuma Akimoto, Yoji Aizawa
    • Journal Title

      Chaos

      Volume: 20

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 弱いカオス系において、エイジングは規則的な運動を生成する2013

    • Author(s)
      秋元琢磨,Eli Barkai
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学
    • Year and Date
      2013-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] 弱いカオス系において、エイジングは規則的な運動を生成する2013

    • Author(s)
      秋元琢磨、Eli Barkai
    • Organizer
      日本物理学会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 速い拡散(レビィウォーク)に外場を加えると分布として応答する2012

    • Author(s)
      秋元琢磨
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2012-09-19
    • Related Report
      2012 Final Research Report
  • [Presentation] 細胞内輸送現象におけるベキ法則と応答理論2012

    • Author(s)
      秋元琢磨
    • 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
      2012-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] 連続時間ランダムウォークにおけるエルゴード性の遅い回復2012

    • Author(s)
      宮口智成,秋元琢磨
    • 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
      2012-03-25
    • Related Report
      2012 Final Research Report
  • [Presentation] 遅い拡散における単一軌道を基にしたアインシュタインの関係の拡張2012

    • Author(s)
      秋元琢磨
    • 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
      2012-03-24
    • Related Report
      2012 Final Research Report
  • [Presentation] 遅い拡散における単一軌道を基にしたアインシュタインの関係の拡張2012

    • Author(s)
      秋元琢磨
    • Organizer
      日本物理学会
    • Place of Presentation
      関西学院大学
    • Year and Date
      2012-03-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] 細胞内輸送現象におけるベキ法則と応答理論2012

    • Author(s)
      秋元琢磨
    • Organizer
      日本物理学会
    • Place of Presentation
      関西学院大学(招待講演)
    • Year and Date
      2012-03-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Applications of infinite ergodic theory in anomalous diffusion2012

    • Author(s)
      Takuma Akimoto
    • Organizer
      ESF-JSPS Frontier Science Conference Series for Young Researchers, Mathematics for innovation : Large and complex systems
    • Place of Presentation
      Tokyo (Japan)
    • Year and Date
      2012-03-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] Applications of infinite ergodic theory in anomalous diffusion2012

    • Author(s)
      T. Akimoto
    • Organizer
      ESF-JSPS Frontier Science Conference Series for Young Researchers, Mathematics for innovation: Large and complex systems
    • Place of Presentation
      Tokyo (Japan)
    • Related Report
      2012 Final Research Report
  • [Presentation] 速い拡散(レヴィウォーク)に外場を加えると分布として応答する2012

    • Author(s)
      秋元琢磨
    • Organizer
      日本物理学会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Relationship between dynamical instability and transport coefficient in anomalous subdiffusion2011

    • Author(s)
      Takuma Akimoto
    • Organizer
      Weak Chaos, Infinite Ergodic Theory, and Anomalous Dynamics
    • Place of Presentation
      Dresden (Germany)
    • Year and Date
      2011-07-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] 一時的劣拡散と切断レビィフライト:エルゴード性のゆっくりとした回復2011

    • Author(s)
      宮口智成,秋元琢磨
    • 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
      2012 Final Research Report
  • [Presentation] 遅い決定論的拡散における輸送係数の揺らぎの理論2011

    • Author(s)
      秋元琢磨,宮口智成
    • Organizer
      日本物理学会第66回年次大会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] 遅い決定論的拡散における輸送係数の揺らぎの理論2011

    • Author(s)
      秋元琢磨、宮口智成
    • Organizer
      日本物理学会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Relationship between dynamical instability and transport coefficient in anomalous subdiffusion2011

    • Author(s)
      T. Akimoto
    • Organizer
      Weak Chaos, Infinite Ergodic Theory, Anomalous Transport
    • Place of Presentation
      Max-Planck Institute (Germany)
    • Related Report
      2012 Final Research Report
  • [Presentation] Intrinsic Randomness of Transport Coefficient in Anomalous Diffusion2010

    • Author(s)
      T.Akimato, T.Miyaguchi
    • Organizer
      The 13th Slovenia-Japan seminar on nonlinear science and Waseda AICS symposium on nonlinear and nonequilibrium phenomena in complex systems
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-11-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Statistical properties of the transport coefficient for deterministic anomalous diffusion2010

    • Author(s)
      T.Akimoto, T.Miyaguchi
    • Organizer
      Anomalous Transport : from Billiards to Nanosystems
    • Place of Presentation
      Sperlonga (Italy)
    • Year and Date
      2010-09-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Intrinsic randomness of transport coefficient in anomalous diffusion2010

    • Author(s)
      T. Akimoto, and T. Miyaguchi
    • Organizer
      The 13th Slovenia-Japan seminar on nonlinear science and Waseda AICS symposium on nonlinear and nonequilibrium phenomena in complex systems
    • Place of Presentation
      Waseda (Japan)
    • Related Report
      2012 Final Research Report
  • [Presentation] Statistical properties of the transport coefficient for deterministic anomalous diffusion2010

    • Author(s)
      T. Akimoto, and T. Miyaguchi
    • Organizer
      Anomalous Transport: from Billiards to Nanosystems
    • Place of Presentation
      Sperlonga (Italy)
    • Related Report
      2012 Final Research Report
  • [Presentation] Mittag-Leffler law for diffusion coefficient in deterministic subdiffusion2010

    • Author(s)
      T. Akimoto, and T. Miyaguchi
    • Organizer
      Dynamics Days Asia Pacific 6
    • Place of Presentation
      Sydney (Australia)
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Remarks]

    • URL

      http://akimototakuma.wordpress.com/

    • Related Report
      2012 Final Research Report
  • [Remarks] HP of Takuma Akimoto

    • URL

      http://akimototakuma.wordpress.com/publications/

    • Related Report
      2012 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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