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Diffusion in a bistable potential

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  • Felderhof, B.U.

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.

Suggested Citation

  • Felderhof, B.U., 2008. "Diffusion in a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5017-5023.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:21:p:5017-5023
    DOI: 10.1016/j.physa.2008.04.034
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    Cited by:

    1. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.

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