The transient case of the quenched trap model

Stanislav Burov

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In this work the anomalous diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder averaged positional probability density function. We establish that the dimensionality and the geometric properties of the lattice, on top of which the disorder is imposed, dictate the plausibility of the approximation that only includes annealed disorder. Specifically, for any case when the probability to return to the origin (Q 0) is less than 1, i.e. the transient case, the quenched trap model can be mapped on to the continuous time random walk. The explicit form of the mapping is provided. In the case when an external force is applied on a tracer particle in a media described by the quenched trap model, the response to such force is calculated and a non-linear response for sufficiently low dimensionality is observed.

Original languageEnglish
Article number073207
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number7
StatePublished - Jul 2020

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  • Brownian motion
  • diffusion
  • driven diffusive systems
  • transport properties


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