Non-Markovian theory of activated rate processes. V. External periodic forces in the low-friction limit

The escape of a particle from a potential well under the influence of both thermal (generalized Langevin) noise and friction and an external periodic driving force is studied in the low-friction limit. We consider three models: (a) additive thermal noise and a completely coherent driving force; (b) additive thermal noise and a phase-diffusing driving force; (c) coherent driving force and multiplicative random noise. The last two models are characterized by dephasing which affects the escape dynamics both qualitatively and quantitatively. In all three cases the escape rate is resonantly enhanced; however, while the first case is characterized by a finite energy peak in the steady-state distribution function, the presence of strong dephasing in the other two cases leads to a generalized Boltzman distribution with an effective temperature which depends resonantly on the external pumping. The relevance of this work to recent experimental results on the resonant activation of a Josephson junction out of its zero-voltage state is discussed.