The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion
Statistical Mechanics
2015-05-19 v2 Chemical Physics
Abstract
We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.
Keywords
Cite
@article{arxiv.1504.06382,
title = {The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion},
author = {Ran Guo and Jiulin Du},
journal= {arXiv preprint arXiv:1504.06382},
year = {2015}
}
Comments
12 pages,6 figures