Transport in disordered systems: The single big jump approach

Wanli Wang, Alessandro Vezzani, Raffaella Burioni, Eli Barkai

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21 Scopus citations


In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits superdiffusion. In the context of glass-forming systems, supercooled glasses, and contamination spreading in porous media, it was suggested that this behavior be modeled with a biased continuous-time random walk. Here we analyze the plume of particles lagging far behind the mean, with the single big jump principle. Revealing the mechanism of the anomaly, we show how a single trapping time, the largest one, is responsible for the rare fluctuations in the system. These nontypical fluctuations still control the behavior of the mean square displacement, which is the most basic quantifier of the dynamics in many experimental setups. We show how the initial conditions, describing either the stationary state or nonequilibrium case, persist forever in the sense that the rare fluctuations are sensitive to the initial preparation. To describe the fluctuations of the largest trapping time, we modify Fréchet's law from extreme value statistics, taking into consideration the fact that the large fluctuations are very different from those observed for independent and identically distributed random variables.

Original languageEnglish
Article number033172
JournalPhysical Review Research
Issue number3
StatePublished - 12 Dec 2019

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© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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