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Escape by diffusion from a square well across a square barrier

✍ Scribed by B.U. Felderhof

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 259 KB
Volume: 387
Category: Article
ISSN: 0378-4371
DOI: 10.1016/j.physa.2007.08.041

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✦ Synopsis

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.

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