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

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...

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Bibliographic Details
Main Author Bocquet, Lydéric
Format Journal Article
LanguageEnglish
Published 30.05.1996
Subjects
Physics - Disordered Systems and Neural Networks
Physics - Materials Science
Physics - Mesoscale and Nanoscale Physics
Physics - Other Condensed Matter
Physics - Quantum Gases
Physics - Soft Condensed Matter
Physics - Statistical Mechanics
Physics - Strongly Correlated Electrons
Physics - Superconductivity
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Summary: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.
DOI:10.48550/arxiv.cond-mat/9605186