ON THE WANG-UHLENBECK PROBLEM IN DISCRETE VELOCITY SPACE

Authors
Citation
Dj. Bicout et A. Szabo, ON THE WANG-UHLENBECK PROBLEM IN DISCRETE VELOCITY SPACE, Journal of statistical physics, 91(5-6), 1998, pp. 1047-1054
Citations number
12
Categorie Soggetti
Physycs, Mathematical","Physycs, Mathematical
ISSN journal
00224715
Volume
91
Issue
5-6
Year of publication
1998
Pages
1047 - 1054
Database
ISI
SICI code
0022-4715(1998)91:5-6<1047:OTWPID>2.0.ZU;2-X
Abstract
The arguably simplest model for dynamics in phase space is the one whe re the velocity can jump between only two discrete values, +/- v, with rate constant k. For this model, which is the continuous-space versio n of a persistent random walk, analytic expressions are found for the first passage lime distributions to the origin. Since the evolution eq uation of this model can be regarded as the two-state finite-differenc e approximation in velocity space of the Kramers-Klein equation, this work constitutes a solution of the simplest version of the Wang-Uhlenb eck problem. Formal solution (in Laplace space) of generalizations whe re the velocity can assume an arbitrary number of discrete states that mimic the Maxwell distribution is also provided.