High-frequency behavior of periodically modulated stochastic quantum system: activated escape

Abstract

We explore the dynamics of a quantum dissipative system subjected to a space dependent, rapidly oscillating periodical force in semiclassical regime. Starting from a time dependent quantum system-reservoir Hamiltonian, we arrive at an effective time independent c-number generalized Langevin equation at leading order using multiple scale perturbation theory which rules the dynamics of the system. The motion for the slow part has been calculated perturbatively in powers of the frequency (ω) of the applied force to the order . We have employed our derived time-independent results to study the escape rate of the modulated system by numerical simulations. To illustrate the impact of driving on the resulting rate in conjunction with the thermal noise, we provide the results without driving and results of the corresponding classical analogue. The escape rate is larger in the presence of driving due to the intricate interplay of spatially periodic gradients, periodic modulation and thermal noise.