Flooding dynamics of diffusive dispersion in a random potential

Michael Wilkinson, Marc Pradas, Gerhard Kling

Research output: Contribution to journalArticlepeer-review


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 $\bar T(x)$, which is an informative description of the typical course of the dispersion, with the expectation value $\langle T(x)\rangle$, which is dominated by rare events where there is an exceptionally high barrier to diffusion. We show that at relatively short times the median $\bar T(x)$ 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.
Original languageEnglish
JournalJournal of Statistical Physics
Publication statusAccepted/In press - 7 Feb 2021


  • disfusion
  • ornstein-Uhlenbeck process

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