Trace of anomalous diffusion in a biased quenched trap model

Abstract

Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drift or the diffusion coefficient remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes zero when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.

arXiv comment8 pages, 5 figures

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• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• Symmetry Breaking of Current Response in Disordered Exclusion Processes