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 $\tau \to 0$ and $\tau \to \infty$, and the agreement with numerics in between is also excellent, both for dichotomic and Gaussian barrier perturbations.