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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Bologna, M., Aquino, G. Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution. Eur. Phys. J. B 87, 15 (2014). https://doi.org/10.1140/epjb/e2013-40701-3
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DOI: https://doi.org/10.1140/epjb/e2013-40701-3