 Escape by diffusion from a parabolic well across a parabolic barrierB.U. Felderhof Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 8, 1767-1785 Abstract: The problem of escape of a particle by diffusion from a parabolic potential well across a parabolic barrier adjacent to free space 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 for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in the well. In the limit of a high barrier the rate of escape is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result. The probability that the particle resides in the well–barrier region at time t decays with a 1/t long-time tail. Keywords: Escape rate; Diffusion; Transition rate; Barrier crossing (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:8:p:1767-1785 DOI: 10.1016/j.physa.2007.11.040 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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