Kramers' law: Validity, derivations and generalisations

Nils Berglund
Markov Processes Relat. Fields 19, 459-490 (2013)

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.

Mathematical Subject Classification: 58J65, 60F10 (primary), 60J45, 34E20 (secondary)

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

 

Journal Homepage Published article MR3156961 Zbl1321.58035

PDF file (328 Kb) hal-00604399 arXiv/1106.5799