Diffusion in a bistable potential |
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Authors: | BU Felderhof |
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Institution: | Institut für Theoretische Physik A, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany |
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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. |
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Keywords: | 82 20 Db 82 20 Uv 44 05+e 73 40 Ty |
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