Asymptotic distributions of Periodically Driven Stochastic Systems

TL;DR

This paper develops a perturbative approach to analyze the long-term behavior of Brownian particles in a viscous medium under rapidly oscillating, position-dependent periodic forces, revealing their asymptotic distribution and oscillatory dynamics.

Contribution

It introduces a high-frequency perturbative method to determine the asymptotic distribution of particles in periodically driven stochastic systems, including second-order corrections.

Findings

Particles oscillate around an effective static potential.

Asymptotic distribution determined to second order.

Effective potential can have complex forms.

Abstract

We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential which can have interesting forms.