Eur. Phys. J. B (2014) 87: 15
https://doi.org/10.1140/epjb/e2013-40701-3

Regular Article

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

¹ Instituto de Alta Investigación, Universidad de Tarapacá-Casilla, 6- D Arica, Chile
² Department of Life Sciences, Imperial College London, SW7 2 AZ London, UK

^a e-mail: g.aquino@imperial.ac.uk

Received: 23 July 2013
Received in final form: 9 October 2013
Published online: 20 January 2014

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.