Kapitza-Landau time window for a periodically driven system with friction: a system-bath Hamiltonian approach

Abstract

We analyze microscopically the classical dynamics of a Brownian particle moving through a damping medium in a confined potential in the presence of random impulses due to the surrounding medium, which is further subjected to a space dependent, high-frequency time-periodic force (with frequency ω). By invoking a systematic separation of time scales using the inverse of driving frequency as the small parameter, starting from a time-dependent system-reservoir model, we derive an effective system-reservoir Hamiltonian (H eff) which does not include explicit time-dependence. H eff yields an effective Langevin description of the system governed by a time-independent effective potential. Here, we want to generalize Kapitza’s treatment for handling time dependent system within the system-reservoir frame. This work may be relevant for trapping of a classical particle with friction by introducing an external rapid time periodic potential. In our present formulation, different species of particles envisage different minima associated with the effective potential, and this is reminiscent of the fact that the effective potential bears explicit information of those parameters that specify the particles. This aspect can be suitably exploited to segregate different species of Brownian particles (that were initially mixed) with the aid of an appropriate driving by a space-dependent periodic force.