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Log-periodic modulation in one-dimensional random walks

L. Padilla, H. O. Mártin and J. L. Iguain

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We 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.


PACS

66.30.-h Diffusion in solids

05.40.Fb Random walks and Levy flights

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Subjects

Condensed matter: structural, mechanical & thermal

Statistical physics and nonlinear systems

Dates

Issue 2 (January 2009)

Received 9 October 2008, accepted for publication 22 December 2008

Published 30 January 2009



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