Mean escape time of ballistically transporting Brownian particles due to thermal noise

Abstract

The mean escape time of Brownian particles from a metastable potential well is investigated under the influence of a thermal time derivative Ornstein–Uhlenbeck noise, which can induce ballistic diffusion of force-free Brownian particles. Compared with the usual Ornstein–Uhlenbeck noise, some new characteristics are obtained. The Brownian particles escape fast remarkably for a larger correlation time of the Ornstein–Uhlenbeck noise. The mean escape time increases as the correlation time decreases, which is contrary to the Ornstein–Uhlenbeck noise case. The escape time for derivative Ornstein–Uhlenbeck noise is longer than that of Ornstein–Uhlenbeck noise for small strength of noise and small correlation time of Ornstein–Uhlenbeck noise. These features are explained by the spectrum features of derivative Ornstein–Uhlenbeck noise and the corresponding dynamical effects.