2020/08/18 by Wilkinson, Michael, Pradas, Marc, Kling, Gerhard
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2008.07854
We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time T(x) to reach position x, arising from different realisations of the random potential: specifically, we contrast the median T(x), which is an informative description of the typical course of the dispersion, with the expectation value ⟨ T(x)⟩, which is dominated by rare events where there is an exceptionally high barrier to diffusion. We show that at relatively short times the median T(x) is explained by a 'flooding' model, where T(x) is predominantly determined by the highest barriers which is encountered before reaching position x. These highest barriers are quantified using methods of extreme value statistics.