Escape over a potential barrier in the presence of colored noise: Predictions of a local-linearization theory

Abstract

The projection-operator method is used to find a Fokker-Planck equation with a time-dependent diffusion coefficient. It is shown that this equation is correct under a precise condition of small noise intensity and can be used successfully to study the problem of escape over the potential barrier of a bistable system. An exact expression for the first-passage time for τ→∞ is found, where τ is the noise correlation time. It is then shown with a numerical method that the Fokker-Planck equation relying on the assumption of local linearization bridges the exact limit for τ→∞ and the standard one for τ=0. Some intriguing aspects of the short-τ region are discussed.