Time oscillations of escape rates in periodically driven systems

We provide an explicit solution of the: problem of activation escape from a metastable state of a periodically driven Brownian particle, including both the exponent and the prefactor. We find the instantaneous and time-average escape rates, and a crossover in their field dependence, from weak to exponentially strong, with amplitude and period of the driving field. The results apply for an arbitrary ratio between the field amplitude and the noise intensity, and between the field period and the relaxation time of the system. [S0031-9007(99)08926-7].