Thermally activated escape with potential fluctuations driven by an Berrnstein-Uhlenbeck process

Abstract

We study the mean escape time T¯ of an overdamped Brownian particle in a metastable potential that is subject to additive Gaussian white noise (thermal noise) and multiplicative Ornstein-Uhlenbeck noise (potential fluctuations). We derive two very general simple conditions for the existence of ‘‘resonant activation,’’ i.e., a minimum of T¯ as a function of the correlation time τ of the potential fluctuations. In the case of small thermal and potential fluctuations, we investigate T¯(τ) for large τ by means of a kinetic model and the remaining τ regime by means of quasipotential theory. We find three different types of ‘‘resonant activation’’: a standard type, a type that typically occurs for potentials without fluctuations near the barrier and the well, and a mixed type.