Diffusion in a bistable potential

✍ Scribed by B.U. Felderhof

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 316 KB
• Volume: 387
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2008.04.034

✦ Synopsis

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.