Superdiffusion in Decoupled Continuous Time Random Walks

Details Superdiffusion in Decoupled Continuous Time Random Walks Superdiffusion in Decoupled Continuous Time Random Walks

2000-07-03

arxiv.org/abs/cond-mat/0007038v1

Physics

Condensed Matter

Statistical Mechanics

9 pages (.tex file), 1 Postscript figures, uses revtex.sty

Scientific paper

10.1016/S0375-9601(01)00234-1

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined)grows as $t^{2/\gamma}$ with $0<\gamma\leq2$ when $t\to \infty$. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of $x^2$ calculated with the corresponding probability distribution behaves exactly as $t^{2/\gamma}$ in the asymptotic limit.

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