Kramers' Law: Validity, Derivations and Generalisations

N. Berglund

2013, v.19, №3, 459-490

ABSTRACT

Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to obtain a mathematically rigorous proof of this formula. We also discuss some generalisations, and a case in which Kramers' law is not valid. This review is written for both mathematicians and theoretical physicists, and endeavours to link concepts and terminology from both fields.

Keywords: Arrhenius' law,Kramers' law,metastability,large deviations,Wentzell - Freidlin theory,WKB theory,potential theory,capacity,cycling,Witten Laplacian