Mean escape time over a fluctuating barrier

An approximate method for studying activation over a fluctuating barrier of potential is proposed. It involves considering separately the slow and fast components of barrier fluctuations, and it applies for any value of their correlation time $\tau .$ It gives exact results for the limiting values $\overrightarrow{\tau }0$ and $\overrightarrow{\tau }\infty ,$ and the agreement with numerics in between is also excellent, both for dichotomic and Gaussian barrier perturbations.