Flooding dynamics of diffusive dispersion in a random potential

Wilkinson, Michael; Pradas, Marc and Kling, Gerhard (2021). Flooding dynamics of diffusive dispersion in a random potential. Journal of Statistical Physics, 182(3), article no. 54.

DOI: https://doi.org/10.1007/s10955-021-02721-5


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 motion, 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 are encountered before reaching position x. These highest barriers are quantified using methods of extreme value statistics.

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