Eyring-Kramers law for Fokker-Planck type differential operators

TL;DR

This paper establishes Eyring-Kramers formulas for the spectral bottom of Fokker-Planck operators linked to Langevin processes, using Gaussian quasimodes without relying on supersymmetry assumptions.

Contribution

It introduces a novel approach to derive Eyring-Kramers formulas for Fokker-Planck operators without supersymmetry or PT-symmetry assumptions.

Findings

Proves Eyring-Kramers formulas in low temperature regime

Constructs sharp Gaussian quasimodes for spectral analysis

Applies to general Langevin processes with Gibbs measures

Abstract

We consider Fokker-Planck type differential operators associated with general Langevin processes admitting a Gibbs stationary distribution. Under assumptions insuring suitable resolvent estimates, we prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the low temperature regime. Our approach is based on the construction of sharp Gaussian quasimodes which avoids supersymmetry or PT-symmetry assumptions.