Rayleigh–Ritz calculation of the activation rate in the spatial diffusion regime

Abstract

We propose a Rayleigh-quotient-based perturbation method for estimating the least nonvanishing eigenvalue of the Fokker–Planck equation in the spatial diffusion regime. Comparison of the resulting expression against exact numerical rates in a symmetric double well produces excellent agreement at all barrier heights. The corresponding relative error is lower by more than an order of magnitude than those of existing finite-barrier expansions.