The role of weak resonances in ac-driven Brownian motion and rate processes

In recent paper a theory of the effect of ac drive on the distribution function and escape rate of a multidimensional underdamped nonlinear oscillator subject to thermal damping and noise was suggested. The approach was based on describing the dynamics in terms of isolated nonlinear resonances and supposing that the noise intensity is asymptotically small,0. In the present work, the case of finite is considered, when weak resonances cannot be described asymptotically. It is shown that forp _r/1(p _r, is the resonance width) the asymptotic results are valid. Forp _r/1, a semiphenomenological theory is developed.