Anomalous diffusion in correlated continuous time random walks
Statistical Mechanics
2015-05-14 v2
Abstract
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0<alpha<=2) give rise to subdiffusion of the form <r^2(t)>~t^{alpha/(1+alpha)}. In contrast correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.
Cite
@article{arxiv.0910.1194,
title = {Anomalous diffusion in correlated continuous time random walks},
author = {Vincent Tejedor and Ralf Metzler},
journal= {arXiv preprint arXiv:0910.1194},
year = {2015}
}
Comments
6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communication