Formulation of variational principle for fractional kinetics and its applications

2017 Fiscal Year Final Research Report

• 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
• Keywords: 非整数運動学 / 変分原理 / 正準形式

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.

Free Research Field

物理学