Asymptotic distributions of Periodically Driven Stochastic Systems

摘要

We study the large-time behaviour of Brownian particles moving through aviscous medium in a confined potential, and which are further subjected toposition-dependent driving forces that are periodic in time. We focus on thecase where these driving forces are rapidly oscillating with an amplitude thatis not necessarily small. We develop a perturbative method for thehigh-frequency regime to find the large-time behavior of periodically drivenstochastic systems. The asymptotic distribution of Brownian particles is thendetermined to second order. To first order, these particles are found toexecute small-amplitude oscillations around an effective static potential whichcan have interesting forms.