Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

Details Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

2003-08-06

arxiv.org/abs/physics/0308023v1

Physics

Atomic Physics

4 pages prevtex4 file, 1 eps figure

Scientific paper

10.1103/PhysRevE.69.022102

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 Schr$\ddot{\rm o}$dinger equation of some quantum mechanical problems.

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