Diffusion in a bistable potential

B.U. Felderhof

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 21, 5017-5023

Abstract: The problem of diffusion of a particle in a bistable potential is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. The potential is modeled as two parabolic wells separated by a parabolic barrier. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells. In the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result.

Keywords: Bistable potential; Barrier crossing; Transition rate (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:21:p:5017-5023

DOI: 10.1016/j.physa.2008.04.034

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