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: This email address is being protected from spambots. You need JavaScript enabled to view it.
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2014
