Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 387, Issue 1, Pages 39-56Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2007.08.041
Keywords
diffusion; escape; heat conduction
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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. (c) 2007 Elsevier B.V. All rights reserved.
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