Log-periodic oscillations for diffusion on self-similar finitely ramified structures
Statistical Mechanics
2015-05-18 v1
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.
Cite
@article{arxiv.1004.0537,
title = {Log-periodic oscillations for diffusion on self-similar finitely ramified structures},
author = {L. Padilla and H. O. Mártin and J. L. Iguain},
journal= {arXiv preprint arXiv:1004.0537},
year = {2015}
}