Multidimensional activated rate processes with slowly relaxing mode

A.M. Berezhkovskii and V.Yu. Zitserman

Physica A: Statistical Mechanics and its Applications, 1992, vol. 187, issue 3, 519-550

Abstract: The multidimensional Kramers problem is considered in the case of highly anisotropic friction. As a development of our previous results involving the study of several new regimes of activated rate process, we construct a theory which incorporates all these regimes and treats the process in every case in a uniform manner. To do this we take advantage of the friction anisotropy and reduce the initial multidimensional Fokker-Planck equation to a set of two effective one-dimensional equations. These equations describe diffusive motion along the slow coordinate in two effective potential wells and inter-well transitions due to the fast coordinate motion. To calculate the rate constant on the basis of the set we use an original method which is a generalization of the Kramers method. As a result we obtain a new formula for the rate constant which depending on the friction anisotropy level is smoothly changed from the well-known Kramers-Langer formula to new ones obtained in our previous papers.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:187:y:1992:i:3:p:519-550

DOI: 10.1016/0378-4371(92)90009-F

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