Diffusion theory of multidimensional activated rate processes: The role of anisotropy

M. M. Kłosek-Dygas*, B. M. Hoffman, B. J. Matkowsky, A. Nitzan, M. A. Ratner, Z. Schuss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We consider an anisotropic multidimensional barrier crossing problem, in the Smoluchowski (diffusion) limit. The anisotropy arises from either or both the shape of the potential energy surface and anisotropic diffusion. In such situations, the separatrix, which separates reactant and product regions of attraction, does not coincide with the ridge of the potential surface, which separates reactant and product wells, thus giving rise to a complicated time evolution. In the asymptotically long time limit, the time evolution is governed by crossing the separatrix and is exponential with a rate which may be obtained as a generalization of Kramers' theory to the anisotropic situation. In contrast, in long, though not asymptotically long times, the time evolution is dominated by repeated crossings of the ridge, and is nonexponential. Such nonexponential time evolution has been observed in many biochemical reactions, where many degrees of freedom and anisotropic diffusion processes lead to complicated dynamical behavior. Our model provides a simple prototype of such situations.

Original languageEnglish
Pages (from-to)1141-1148
Number of pages8
JournalThe Journal of Chemical Physics
Issue number2
StatePublished - 1989


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