Flooding dynamics of diffusive dispersion in a random potential

Michael Wilkinson* (Corresponding Author), Marc Pradas, Gerhard Kling

*Corresponding author for this work

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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
Article number54
JournalJournal of Statistical Physics
Early online date5 Mar 2021
Publication statusPublished - 2021

Bibliographical note

Acknowledgments. We thank Baruch Meerson for bringing [4] to our notice, and for interesting discussion about the statistics of barrier heights. MW thanks the Chan-Zuckerberg Biohub for their hospitality


  • diffusion
  • Ornstein-Uhlenbeck process


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