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The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion

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.

preprint2015arXivOpen access
Ran GuoJiulin Du
cond-mat.stat-mechphysics.chem-ph
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Ran GuoJiulin Du

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