Geometric Characterization of the Eyring-Kramers Formula
Abstract
In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate this is in the low noise regime exactly characterized by the so called Eyring-Kramers law and gives the mean transition time as a quantity depending on the curvature of the minima and the saddle. In this paper we find an extension of the Eyring-Kramers law giving an upper bound on the mean transition time when both the minima/saddles are degenerate (flat) while at the same time covering multiple saddles at the same height. Our main contribution is a new sharp characterization of the capacity of two local minimas as a ratio of two geometric quantities, i.e., the smallest separating surface and the geodesic distance.
Keywords
Cite
@article{arxiv.2206.13206,
title = {Geometric Characterization of the Eyring-Kramers Formula},
author = {Benny Avelin and Vesa Julin and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2206.13206},
year = {2022}
}