Escape by diffusion from a square well across a square barrier

B.U. Felderhof

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 1, 39-56

Abstract: The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.

Keywords: Diffusion; Escape; Heat conduction (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:1:p:39-56

DOI: 10.1016/j.physa.2007.08.041

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