%0 Journal Article
%T Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media
%A V. Ilyin
%A I. Procaccia
%A A. Zagorodny
%J Condensed Matter Physics
%D 2013
%I Institute for Condensed Matter Physics
%X 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.
%K non-Markovian processes
%K fractional diffusion
%K ballistic effects
%U http://dx.doi.org/10.5488/CMP.16.13004