Diffusion in Flashing Periodic Potentials

TL;DR

This paper derives exact formulas for the effective diffusion coefficient of Brownian particles in symmetric periodic potentials modulated by external noise, revealing conditions for diffusion acceleration and finite net diffusion without thermal noise.

Contribution

It provides general equations for calculating effective diffusion in supersymmetric potentials modulated by white Gaussian or Markovian dichotomous noise, including new analytical expressions.

Findings

Diffusion accelerates in fast fluctuating potentials and sawtooth potentials.

Finite net diffusion occurs without thermal noise.

Rectangular potentials slow down diffusion compared to free diffusion.

Abstract

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated: (i) by external white Gaussian noise and (ii) by Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down in comparison with the case when particles diffuse freely, for all parameters of noise and of potential.