L. Padilla et al 2009 EPL 85 20008 doi:10.1209/0295-5075/85/20008
L. Padilla, H. O. Mártin and J. L. Iguain
Show affiliationsWe have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law modulated by logarithmic periodic oscillations. The origin of this modulation is due to the dependence of the diffusion coefficient on the length scale. Both the random walk exponent and the period of the modulation are analytically calculated and confirmed by Monte Carlo simulations.
05.40.Fb Random walks and Levy flights
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 2 (January 2009)
Received 9 October 2008, accepted for publication 22 December 2008
Published 30 January 2009
L. Padilla et al 2009 EPL 85 20008
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