Abstract
The Brownian motion of a particle over a potential barrier, a problem first solved by Kramers, is reexamined also for the case of “intermediate” friction, to which Kramers' solutions do not apply. The theory is macroscopic and entirely based on the Langevin equation of the particle, but it makes essential use of ideas of a recent microscopic theory of Grabert and of Pollak, Grabert, and Hänggi for a particle coupled to an infinite set of harmonic oscillators. Their result for the escape rate is recovered, but the present method seems more generally applicable. We introduce and use a new theoretical tool-the transformation to a new set of variables mixing the macroscopic and the noise variables of the Langevin equation.
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Graham, R. Macroscopic theory of activated decay of metastable states. J Stat Phys 60, 675–694 (1990). https://doi.org/10.1007/BF01025989
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DOI: https://doi.org/10.1007/BF01025989