Controlling activated processes of nonadiabatically, periodically driven dynamical systems: a multiple scale perturbation approach.
We arrive at the escape rate from a metastable state for a system of Brownian particles driven periodically by a space dependent, rapidly oscillating external perturbation (with frequency ω) in one dimension (one of the most important class of nonequilibrium system). Though the problem may seem to be time-dependent, and is poised on the extreme opposite side of adiabaticity, there exists a multiple scale perturbation theory ("Kapitza window") by means of which the dynamics can be treated in terms of an effective time-independent potential that is derived as an expansion in orders of 1/ω to the order ω(-3). The resulting time-independent equation is then used to calculate the escape rate of physical systems from a metastable state induced by external monochromatic field in the moderate-to-large damping limit and to investigate the effect of ω on the resulting rate in conjunction with the thermal energy. With large value of ω, we find that the environment with moderate-to-large damping impedes the escape process of the particle while high amplitude of the periodic driving force allows the particle to cross the barrier with a large escape rate. A comparison of our theoretical expression with numerical simulation gives a satisfactory agreement.
Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
Anindita
A
Shit
Sudip
S
Chattopadhyay
Jyotipratim
J
Ray Chaudhuri