Random walks in fractal media: A theoretical evaluation of the periodicity of the oscillations in dynamic observables

A. MALTZ; G. FABRICIUS; M. A. BAB; E. V. ALBANO

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

Institut of Physics Publishing

Año: 2008 vol. 41 p. 495004 - 495016

0305-4470

In this work we address the time evolution of random walks on a special type of Sierpinski carpets, which we call Walk Similar (WS). By considering highly symmetric fractals (symmetrically self-similar graphs (SSG)), very recently Kron and E. Teu (Trans. AMS. 356, 393 (2003)) have developed a technique based on the fact that the random walk gives rise to an equivalent process in a similar subset. The method is used in order to obtain the time scaling factor (tau) as the average passing time (APT) of the walker from a site in the subset to any different site in the subset. For SSG, the APT is independent of the starting point. In the present work we generalize this technique under the less stringent symmetry conditions of the WS carpets, such that the APT depends on the starting point. Therefore, we exactly calculate the weighted APT(tau*). By performing Monte Carlo simulations on several WS carpets we verify that tau* plays the role of tau by setting the logarithmic period of the oscillatory asymptotic behavior of dynamic observables.