Formulation of variational principle for fractional kinetics and its applications

• Project/Area Number: 26400391
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Mie 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: ¥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.

Research Products

• [Int'l Joint Research] アリゾナ州立大学(米国)
• [Int'l Joint Research] 華僑大学(中国)
• [Int'l Joint Research] Arizona State University(米国)
• [Int'l Joint Research] University of British Columbia(カナダ)
• [Int'l Joint Research] Huaqiao University(中国)
• [Int'l Joint Research] カザン連邦大学(ロシア連邦)
• [Journal Article] Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems (2017)
  • 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
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Invariants of Fokker-Planck equations (2017)
  • 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
  • Peer Reviewed
• [Journal Article] Subdiffusion of volcanic earthquakes (2017)
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Path probability of stochastic motion: A functional approach (2016)
  • Author(s): M. Hattori and S. Abe
  • Journal Title: Physica A Volume: 451 Pages: 198-204
  • DOI: 10.1016/j.physa.2016.01.053
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Exotic properties and optimal control of quantum heat engine (2016)
  • Author(s): C. Ou and S. Abe
  • Journal Title: EPL Volume: 113 Issue: 4 Pages: 40009-40009
  • DOI: 10.1209/0295-5075/113/40009
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Time evolution of Renyi entropy under the Lindblad equation (2016)
  • Author(s): S. Abe
  • Journal Title: Physical Review E Volume: 94 Issue: 2 Pages: 022106-022106
  • DOI: 10.1103/physreve.94.022106
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fluctuation theorems and 1/f noise from a simple matrix (2016)
  • 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
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Weak invariants of time-dependent quantum dissipative systems (2016)
  • Author(s): S. Abe
  • Journal Title: Physical Review A Volume: 94 Issue: 3 Pages: 032116-032116
  • DOI: 10.1103/physreva.94.032116
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the variational principle for fractional kinetic theory (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Universal clustering structure and C~0.85 scaling in complex earthquake networks (2015)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: Physica A Volume: 421 Pages: 343-346
  • DOI: 10.1016/j.physa.2014.11.001
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Phase-space representation of completely positive quantum operation: Invertible subdynamics of two-mode squeezed states (2015)
  • 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
  • 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
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Anomalous diffusion of volcanic earthquakes (2015)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: EPL Volume: 110 Issue: 5 Pages: 59001-59001
  • DOI: 10.1209/0295-5075/110/59001
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Clifford numbers from Bohr-Sommerfeld quantization of Grassmann-variant systems (2015)
  • Author(s): S. Abe and D. A. Tayurskii
  • Journal Title: JETP Letters Volume: 102 Issue: 6 Pages: 387-390
  • DOI: 10.1134/s0021364015180022
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics (2014)
  • Author(s): S. Abe
  • Journal Title: EPL Volume: 108 Issue: 4 Pages: 40008-40008
  • DOI: 10.1209/0295-5075/108/40008
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Completely-positive quantum operations generating thermostatistical states: A comparative study (2014)
  • Author(s): Y. Matsuo and S. Abe
  • Journal Title: Physica A Volume: 409 Pages: 130-137
  • DOI: 10.1016/j.physa.2014.04.044
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fokker-Planck theory of nonequilibrium systems governed byhierarchical dynamics (2014)
  • Author(s): S. Abe
  • Journal Title: Foundations of Physics Volume: 44 Issue: 2 Pages: 175-182
  • DOI: 10.1007/s10701-014-9775-3
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Renyi entropy rate under Lindblad equation (2017)
  • Author(s): S. Abe
  • Organizer: The 14th Joint European Thermodynamics Conference (May 21-25, 2017, Budapest, Hungary)
  • Int'l Joint Research / Invited
• [Presentation] C-MaxEnt and Bayesian Approach to Extreme Values (2017)
  • Author(s): S. Abe
  • Organizer: The 5th International Workshop On Statistical Physics and Mathematics for Complex Systems (October 12-15, 2017, Wuhan, China)
  • Int'l Joint Research / Invited
• [Presentation] Estimating entanglement in a class of N-qudit states (2017)
  • Author(s): S. Abe
  • Organizer: The International Kazan Conference on Probability Theory and Mathematical Statistics (November 7-10, 2017, Kazan, Russia)
  • Int'l Joint Research / Invited
• [Presentation] Anomalous diffusion in volcanic seismicity (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Anomalous Diffusion in Volcanic Seismicity (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Quantum-Mechanical Analog of the Carnot Engine: Efficiency and Maximum-Power Condition (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Variational Principle for Fractional Kinetics and Anomalous Diffusion (2014)
  • 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
  • Invited