An Extension of the Kramers Rate Theory to Cusped and Smooth Potentials

概要

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The therrnallv arctix'ated escape of a Browniatn p;trticle over an energy baxrrier of arbitrary shapeis considered. Based on the expansion of the underlying Fokker-Planck eqtration in reciprocalpowers of tlae friction constant a rate expression is constrtrcted. It agrees in the limiting case ofltigh friction xvith the rate follow'ing frotta the corresponding Smoltrchowski eqtration and, in theliunit of weak t'riction with the rate obtained front transition state theory. Its acctrracy is testedf'or Brownian motion over a paralcolic barrier in which case we cotaapare to the known analyticKrauaaers restrlt. Apjclications to cusp slaaped and qtrartic barriers show that the approxinaaterate expression is in very good agreenaent with acctrrate estiuaaates of the rates fronn nv.rmericalsitntrlations. An overall rate expression valid in the xvhole f'riction range is then obtained by trsingtlae R/Iel'nikov-lVIeshkov restrlt for the trnderdataaped Brownian utuotion, along with a properlydefined energy loss of tlae particle per oscills'ttiora. Its validity is tested by couaapar'ing with exactnumerical rates in a ctrsped dovrble xvell potential.
社団法人日本物理学会の論文
1999-07-15