Noise-induced escape of periodically modulated systems : From weak to strong modulation

Noise-induced escape from a metastable state is studied for an overdamped periodically modulated system. We develop an asymptotic technique that gives both the instantaneous and period-average escape rates, including the prefactor, for an arbitrary modulation amplitude A. We find the parameter range where escape is strongly synchronized and the instantaneous escape rate displays sharp peaks. The peaks vary with increasing modulation frequency or amplitude from Gaussian to strongly asymmetric. The prefactor in the periodaverage escape rate depends on A nonmonotonically. Near the bifurcation amplitude Ac it scales as Ac  A. We identify three scaling regimes, with =1/4, 1, and 1/2. I. INTRODUCTION Noise-induced escape from a metastable state is an interesting effect of the interplay of nonlinear dynamics and fluctuations that has been attracting much attention since the Kramers paper 1. Escape and the resulting interstate switching are becoming increasingly more important for applications, particularly in nanotechnology where the size of the system is small and fluctuations are comparatively large. Recently much work on escape has been done for systems driven by time-dependent fields. Examples include transitions in modulated nano- and micromechanical oscillators 2,3, Josephson junctions 4‐6, and nanomagnets 7‐9. Modulation changes the activation barrier. This enables both efficient control of the escape rate and accurate measurement of the system parameters 2,10. Because in escape the system moves far away from its metastable states, studying escape provides an insight into the global dynamics of the system. The most frequently used types of modulation are ramping of a control parameter and periodic modulation. Ramping is usually done slowly, and it is assumed that the system remains quasistationary 11. Periodic modulation is conceptually simpler as periodic metastable states are well defined irrespective of the modulation frequency. However, a theory of the escape rate is more complicated, because the system is away from thermal equilibrium 12. Recently significant attention was attracted also to escape over a randomly fluctuating barrier 13,14. In the present paper we study periodically modulated systems and extend to them the analysis of the escape rate done by Kramers for systems in thermal equilibrium 1. Our approach gives the full time-dependent escape rate Wt as well