Unbiased diffusion of Brownian particles on disordered correlated potentials

TL;DR

This study derives an exact formula for the diffusion coefficient of overdamped particles on disordered correlated potentials, revealing that unbiased diffusion is independent of potential correlations due to fundamental physical principles.

Contribution

The paper provides an exact expression for the diffusion coefficient and demonstrates its independence from correlations in disordered potentials, supported by analytical and numerical evidence.

Findings

Diffusion coefficient is independent of potential correlations.

Exact analytical expression for diffusion coefficient derived.

Numerical simulations confirm theoretical predictions.

Abstract

In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us to prove that the unbiased diffusion of overdamped particles on a random polymer does not depend on the correlations of the disordered potentials. This universal behavior of the unbiased diffusivity is a direct consequence of the validity of the Einstein relation and the decay of correlations of the random polymer. We test the independence on correlations of the diffusion coefficient for correlated polymers produced by two different stochastic processes, a one-step Markov chain and the expansion-modification system. Within the accuracy of our simulations, we found that the numerically obtained diffusion coefficient for these systems agree with the analytically calculated ones, confirming our predictions.