Anomalous diffusion in correlated continuous time random walks

Details Anomalous diffusion in correlated continuous time random walks Anomalous diffusion in correlated continuous time random walks

2009-10-07

arxiv.org/abs/0910.1194v2

Physics

Condensed Matter

Statistical Mechanics

6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communication

Scientific paper

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 ~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0~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.

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