Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: A time-independent approach

Abstract

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.