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Diffusion in a time-dependent external field.

Authors
Type
Published Article
Journal
Physical review. E, Statistical, nonlinear, and soft matter physics
Publication Date
Volume
77
Issue
1 Pt 1
Pages
11107–11107
Identifiers
PMID: 18351818
Source
Medline

Abstract

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced by Trigger and co-authors [S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, Physica A 347, 77 (2005); J. Phys.: Conf. Ser. 11, 37 (2005)]. We consider the case of the quasi-Fokker-Planck approximation, when the probability transition function for diffusion (PTD function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.

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