Diffusion and Creep of a Particle in a Random Potential

TL;DR

This paper studies the long-time diffusive behavior of a particle in a 1D random potential, revealing a log-time diffusion law, and analyzes the effects of metastable states and external forces on particle dynamics.

Contribution

It introduces an efficient method using mean first-passage times to analyze large-time dynamics and relates diffusion characteristics to potential details, including non-Gaussian correlations.

Findings

Log-time diffusion characterized by parameters A, β, t_r.

Distribution of first-passage times exhibits intermittency.

Decay of metastable states explains diffusion behavior.

Abstract

We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of the particle. We determine the $log$-time diffusion ${<{< x^{2}(t)>}_{th}>}_{dis}=A\ln^{\beta} \left ({t}/{t_{r}})$ and relate the prefactor $A,$ the relaxation time $t_{r},$ and the exponent $\beta$ to the details of the (generally non-gaussian) long-range correlated potential. Calculating the moments ${<{< t^{n}>}_{th}>}_{dis}$ of the first-passage time distribution $P(t),$ we reconstruct the large time distribution function itself and draw attention to the phenomenon of intermittency. The results can be easily interpreted in terms of the decay of metastable trapped states. In addition, we present a simple derivation of the mean velocity of a particle moving in a random potential in the presence of a constant external force.