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arXiv · 1312.1274

Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution

Mauro Bologna·Gerardo Aquino
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Abstract

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution $ψ(τ)$ of residence times in each velocity state. We obtain analytical solutions for the diffusion process in a generic external potential and for a generic statistics of residence times, including the non-ergodic regime in which the mean residence time diverges. We show that these analytical solutions are in agreement with numerical simulations.

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Mauro Bologna, Gerardo Aquino. 2013-12-04. Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution. https://doi.org/10.1140/epjb%2Fe2013-40701-3

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