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arXiv · 1004.0537

Log-periodic oscillations for diffusion on self-similar finitely ramified structures

L. Padilla·H. O. Mártin·J. L. Iguain
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Abstract

Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order. On these media, the time dependence of the mean-square displacement shows log-periodic modulations around a leading power law, which can be understood on the base of a hierarchical set of diffusion constants. Both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples, one fractal, the other non-fractal, and confirmed by Monte Carlo simulations.

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L. Padilla, H. O. Mártin, J. L. Iguain. 2010-04-04. Log-periodic oscillations for diffusion on self-similar finitely ramified structures. https://doi.org/10.1103/physreve.82.011124

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