Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media

The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non- Markovian...

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Bibliographic Details
Date:2013
Main Authors: Ilyin, V., Procaccia, I., Zagorodny, A.
Format: Article
Language:English
Published: Інститут фізики конденсованих систем НАН України 2013
Series:Condensed Matter Physics
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/121086
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media / V. Ilyin, I. Procaccia, A. Zagorodny // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13004:1–18. — Бібліогр.: 36 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non- Markovian kinetic coefficients are determined by the observable quantities (mean- and mean square displacements). Solutions of the non-Markovian equation describing diffusive processes in the physical space are obtained. For long times these solutions agree with the predictions of continuous random walk theory; they are however much superior at shorter times when the effect of the ballistic behavior is crucial.