A Multiscale Approach to Brownian Motors

TL;DR

This paper develops multiscale methods to analyze Brownian motion in periodic potentials under external forces, deriving formulas for particle current and diffusion, and validating results with numerical simulations.

Contribution

Introduces multiscale techniques to derive general formulas for steady state current and diffusion tensor in driven Brownian systems, with applications to combined Gaussian white and colored noise.

Findings

Derived formulas for steady state particle current and diffusion tensor.

Calculated effective diffusion coefficient for particles under combined noise.

Validated theoretical results with numerical simulations.

Abstract

The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady state particle current and the effective diffusion tensor. These formulae are then applied to calculate the effective diffusion coefficient for a Brownian particle in a periodic potential driven simultaneously by additive Gaussian white and colored noise. Our theoretical findings are supported by numerical simulations.