Quantum escape in the presence of a time-periodic oscillating force

¹ Department of Chemistry, Bengal Engineering and Science University - Shibpur, Howrah-711103, India
² Department of Physics, Katwa College - Katwa, Burdwan-713130, India

^a sudip_chattopadhyay@rediffmail.com
^b jprc_8@yahoo.com

Received: 29 September 2011
Accepted: 18 January 2012

Abstract

The stochastic dynamics of a Brownian particle driven by a space-dependent, rapidly oscillating time-periodic potential (with frequency ω) has been addressed in the quantum regime within the framework of time-dependent system-reservoir Hamiltonian. Employing Floquet theorem in conjunction with the idea of separation of time scales, we construct a Langevin equation (containing a static effective potential) by exploiting a systematic perturbative expansion in powers of ω^{− 1}. We compute the escape rate from the meta-stable state using the corresponding quantum Smoluchowski equation and observe a “resonance phenomenon" which is a signature of system-reservoir quantization. This work can be used to model the trapping mechanism as well as the quantum-fluctuation–induced escape process from the trap.