Anomalous diffusion in a space- and time-dependent energy landscape

Details Anomalous diffusion in a space- and time-dependent energy landscape Anomalous diffusion in a space- and time-dependent energy landscape

2010-11-10

arxiv.org/abs/1011.2284v2

J. Stat. Mech. (2010) P12013

Physics

Condensed Matter

Statistical Mechanics

17 pages, 5 figures. Minor corrections

Scientific paper

10.1088/1742-5468/2010/12/P12013

We study the influence on diffusion in one dimension of a potential energy perturbation varying as a power in space and time. We concentrate on the case of a parabolic perturbation in space decaying as $t^{-\omega}$ which shows a rich variety of scaling behaviours. When $\omega=1$, the perturbation is truly marginal and leads to anomalous (super)diffusion with a dynamical exponent varying continuously with the perturbation amplitude below some negative threshold value. For slower decay, $\omega<1$, the perturbation becomes relevant and the system is either subdiffusive for an attractive potential or displays a stretched-exponential behaviour for a repulsive one. Exact results are obtained for the mean value and the variance of the position as well as for the surviving probability.

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