On the variational principle for fractional kinetic theory

4th International Workshop on Statistical Physics and Mathematics for Complex Systems

物理学;数学

Abe, Sumiyoshi^1,2 ; Oohata, Akifumi^1

Department of Physical Engineering, Mie University, Mie

514-8507, Japan^1

Institute of Physics, Kazan Federal University, Kazan

420008, Russia^2

关键词: Action functional;    Approximate analytic solutions;    Auxiliary-fields;    Fractional Fokker-Planck equation;    Fractional kinetic theory;    Variational principles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/604/1/012001/pdf
DOI  :  10.1088/1742-6596/604/1/012001

来源: IOP

【 摘 要 】

In a recent paper (Abe S 2013 Phys. Rev. E 88 022142), a variational principle has been formulated for spatiotemporally-fractional Fokker-Planck equations and applied to derivations of their approximate analytic solutions based on the Lévy Ansatz. Here, the problem of the constraint associated with normalization condition on a probability distribution behind the principle is discussed. It is shown that the action functional possesses a specific transformation property in terms of an auxiliary field and the constraint turns out to have already been imposed implicitly in terms of such a structure.