Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
Abstract
We study the continuous limit of a multibox Erhenfest urn model proposed before by the authors. The evolution of the resulting continuous system is governed by a differential equation, which describes a diffusion process on a circle with a nonzero drifting velocity. The short time behavior of this diffusion process is obtained directly by solving the equation, while the long time behavior is derived using the Poisson summation formula. They reproduce the previous results in the large M (number of boxes) limit. We also discuss the connection between this diffusion equation and the Schrödinger equation of some quantum mechanical problems.
 Publication:

Physical Review E
 Pub Date:
 February 2004
 DOI:
 10.1103/PhysRevE.69.022102
 arXiv:
 arXiv:physics/0308023
 Bibcode:
 2004PhRvE..69b2102L
 Keywords:

 05.20.y;
 02.50.Ey;
 02.50.r;
 64.60.Cn;
 Classical statistical mechanics;
 Stochastic processes;
 Probability theory stochastic processes and statistics;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Physics  Atomic Physics;
 Physics  General Physics
 EPrint:
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