Resonant activation over a fluctuating barrier

We consider the problem of thermally activated potential barrier crossing in the presence of fluctuations of the barrier itself. For piecewise linear barrier switching between two values as a Markov process, exact and Monte Carlo results reveal a novel resonantlike phenomenon as a function of the barrier fluctuation rate. For very slow variations the average crossing time is the average of the times required to diffuse over each of the barriers separately; for very fast variations the mean crossing time is that required to cross the average barrier. At intermediate rates the crossing is strongly correlated with the potential variation and the escape rate exhibits a local maximum at a ‘‘resonant’’ fluctuation rate.