High friction limit of the Kramers equation : the multiple time-scale approach

Details High friction limit of the Kramers equation : the multiple time-scale approach High friction limit of the Kramers equation : the multiple time-scale approach

1996-05-30

arxiv.org/abs/cond-mat/9605186v1

Physics

Condensed Matter

14 pages, accepted in American Journal of Physics

Scientific paper

10.1119/1.18507

The purpose of the paper is to give a pedagogical introduction to the multiple time-scale technique, on the example of the high friction limit of the Kramers equation. We begin with a discussion of the standard perturbation technique as presented in van Kampen's reference book \refto{VK}, which will be shown to fail in the long-time limit. Application of the multiple time-scale technique avoids these difficulties and leads to a uniform expansion in powers of the inverse of the friction. Analogy with the Chapman-Enskog expansion is discussed.

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