Transport in randomly-fluctuating spatially-periodic potentials

TL;DR

This paper investigates the dynamics of overdamped particles in a spatially-periodic potential with random temporal fluctuations, revealing regimes of near-deterministic motion and trapping, and develops analytical methods to characterize their drift and diffusion behaviors.

Contribution

It introduces perturbation and asymptotic techniques to analyze particle transport in randomly-fluctuating periodic potentials, bridging numerical observations with theoretical understanding.

Findings

Identification of two distinct motion regimes: free-running and trapped.

Development of analytical expressions for drift velocity and diffusion coefficient.

Numerical validation of theoretical predictions.

Abstract

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical aimulations show two distinct parameter regimes, corresponding to free-running near-deterministic particles, and particles which are trapped in local minima of the potential with intermittent escape flights. Perturbation and asymptotic methods are developed to understand the drift velocity and diffusion coefficient in each parameter regime.