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Formulation of variational principle for fractional kinetics and its applications

Research Project

Project/Area Number 26400391
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionMie University

Principal Investigator

ABE Sumiyoshi  三重大学, 工学研究科, 教授 (70184215)

Research Collaborator SUZUKI Norikazu  
OU Congjie  
CHAMBERLIN Ralph V.  
LYSOGORSKIY Yury V.  
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords非整数運動学 / 変分原理 / 正準形式 / 非整数Fokker-Planck方程式 / 異常拡散 / Hamilton形式 / 劣拡散 / 連続時間ランダムウォーク / エントロピー生成率の下限 / 非ユニタリーダイナミクス
Outline of Final Research Achievements

The variational principle has been formulated for the fractional Fokker-Planck equation. In the construction of the action integral, the relation has been revealed between the constraint on the normalization condition on a probability distribution and a gauge-theoretic structure associated with the auxiliary field introduced in the action integral.
In addition, the canonical theory has been constructed, and the fractional Fokker-Planck equation has been recast into the form of the Liouville equation. There, a novel problem concerning the presence of two different Hamiltonians has appeared. Regarding this point, the non-equal-time Poisson-Dirac bracket relations have been set up, and, based on them, it has been shown that the two different Hamiltonians actually generate identical time evolution.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (30 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (6 results) Journal Article (17 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 17 results,  Acknowledgement Compliant: 15 results,  Open Access: 1 results) Presentation (7 results) (of which Int'l Joint Research: 6 results,  Invited: 7 results)

  • [Int'l Joint Research] アリゾナ州立大学(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] 華僑大学(中国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Arizona State University(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] University of British Columbia(カナダ)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Huaqiao University(中国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] カザン連邦大学(ロシア連邦)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems2017

    • Author(s)
      C. Ou, R. V. Chamberlin, and S. Abe
    • Journal Title

      Physica A

      Volume: 466 Pages: 450-454

    • DOI

      10.1016/j.physa.2016.09.016

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Invariants of Fokker-Planck equations2017

    • Author(s)
      S. Abe
    • Journal Title

      European Physical Journal: Special Topics

      Volume: 226 Issue: 3 Pages: 529-532

    • DOI

      10.1140/epjst/e2016-60215-1

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Subdiffusion of volcanic earthquakes2017

    • Author(s)
      Sumiyoshi Abe, Norikazu Suzuki
    • Journal Title

      Acta Geophysica

      Volume: 印刷中 Issue: 3 Pages: 481-489

    • DOI

      10.1007/s11600-017-0029-6

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Path probability of stochastic motion: A functional approach2016

    • Author(s)
      M. Hattori and S. Abe
    • Journal Title

      Physica A

      Volume: 451 Pages: 198-204

    • DOI

      10.1016/j.physa.2016.01.053

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Exotic properties and optimal control of quantum heat engine2016

    • Author(s)
      C. Ou and S. Abe
    • Journal Title

      EPL

      Volume: 113 Issue: 4 Pages: 40009-40009

    • DOI

      10.1209/0295-5075/113/40009

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Time evolution of Renyi entropy under the Lindblad equation2016

    • Author(s)
      S. Abe
    • Journal Title

      Physical Review E

      Volume: 94 Issue: 2 Pages: 022106-022106

    • DOI

      10.1103/physreve.94.022106

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fluctuation theorems and 1/f noise from a simple matrix2016

    • Author(s)
      R. V. Chamberlin, S. Abe, B. F. Davis, P. E. Greenwood, and A. S. H. Shevchuk
    • Journal Title

      European Physical Journal B

      Volume: 89 Issue: 9 Pages: 185-185

    • DOI

      10.1140/epjb/e2016-70242-0

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Weak invariants of time-dependent quantum dissipative systems2016

    • Author(s)
      S. Abe
    • Journal Title

      Physical Review A

      Volume: 94 Issue: 3 Pages: 032116-032116

    • DOI

      10.1103/physreva.94.032116

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the variational principle for fractional kinetic theory2015

    • Author(s)
      S. Abe and A. Oohata
    • Journal Title

      Journal of Physics: Conference Series

      Volume: 604 Pages: 012001-012001

    • DOI

      10.1088/1742-6596/604/1/012001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Universal clustering structure and C~0.85 scaling in complex earthquake networks2015

    • Author(s)
      S. Abe and N. Suzuki
    • Journal Title

      Physica A

      Volume: 421 Pages: 343-346

    • DOI

      10.1016/j.physa.2014.11.001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Phase-space representation of completely positive quantum operation: Invertible subdynamics of two-mode squeezed states2015

    • Author(s)
      S. Abe and Y. Matsuo
    • Journal Title

      Physical Review E

      Volume: 91 Issue: 1 Pages: 012126-012126

    • DOI

      10.1103/physreve.91.012126

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reply to Comment on 'Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle'2015

    • Author(s)
      S. Abe
    • Journal Title

      Physical Review E

      Volume: 91 Issue: 5 Pages: 056102-056102

    • DOI

      10.1103/physreve.91.056102

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Anomalous diffusion of volcanic earthquakes2015

    • Author(s)
      S. Abe and N. Suzuki
    • Journal Title

      EPL

      Volume: 110 Issue: 5 Pages: 59001-59001

    • DOI

      10.1209/0295-5075/110/59001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Clifford numbers from Bohr-Sommerfeld quantization of Grassmann-variant systems2015

    • Author(s)
      S. Abe and D. A. Tayurskii
    • Journal Title

      JETP Letters

      Volume: 102 Issue: 6 Pages: 387-390

    • DOI

      10.1134/s0021364015180022

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics2014

    • Author(s)
      S. Abe
    • Journal Title

      EPL

      Volume: 108 Issue: 4 Pages: 40008-40008

    • DOI

      10.1209/0295-5075/108/40008

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Completely-positive quantum operations generating thermostatistical states: A comparative study2014

    • Author(s)
      Y. Matsuo and S. Abe
    • Journal Title

      Physica A

      Volume: 409 Pages: 130-137

    • DOI

      10.1016/j.physa.2014.04.044

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fokker-Planck theory of nonequilibrium systems governed byhierarchical dynamics2014

    • Author(s)
      S. Abe
    • Journal Title

      Foundations of Physics

      Volume: 44 Issue: 2 Pages: 175-182

    • DOI

      10.1007/s10701-014-9775-3

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Renyi entropy rate under Lindblad equation2017

    • Author(s)
      S. Abe
    • Organizer
      The 14th Joint European Thermodynamics Conference (May 21-25, 2017, Budapest, Hungary)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] C-MaxEnt and Bayesian Approach to Extreme Values2017

    • Author(s)
      S. Abe
    • Organizer
      The 5th International Workshop On Statistical Physics and Mathematics for Complex Systems (October 12-15, 2017, Wuhan, China)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Estimating entanglement in a class of N-qudit states2017

    • Author(s)
      S. Abe
    • Organizer
      The International Kazan Conference on Probability Theory and Mathematical Statistics (November 7-10, 2017, Kazan, Russia)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Anomalous diffusion in volcanic seismicity2016

    • Author(s)
      S. Abe
    • Organizer
      Solvay Workshop - Bridging the gaps at the PCB interface "Multiscale Modelling in Physics, Chemistry and Biology"
    • Place of Presentation
      Brussels (Belgium)
    • Year and Date
      2016-04-19
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Anomalous Diffusion in Volcanic Seismicity2015

    • Author(s)
      S. Abe
    • Organizer
      Complex Systems ― Digital Campus 2015, World e-Conference UNESCO UniTwin
    • Place of Presentation
      インターネット上
    • Year and Date
      2015-09-30
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum-Mechanical Analog of the Carnot Engine: Efficiency and Maximum-Power Condition2015

    • Author(s)
      S. Abe
    • Organizer
      The 6th International Conference on Mechanical Science and Engineering
    • Place of Presentation
      Qingdao, Chin
    • Year and Date
      2015-07-17
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Variational Principle for Fractional Kinetics and Anomalous Diffusion2014

    • Author(s)
      S. Abe
    • Organizer
      The 4th International Workshop On Statistical Physics and Mathematics for Complex Systems
    • Place of Presentation
      Yichang (China)
    • Year and Date
      2014-10-12 – 2014-10-16
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2022-06-07  

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