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

ALBERTO MALTZ; GABRIEL FABRICIUS; MARISA BAB; EZEQUIEL ALBANO

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2008 vol. 41 p. 495004 - 495016

1751-8113

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 Krön and Teufl (2003 Trans. Am. Math. Soc. 356 393) 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 (τ) 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 calculate exactly the weighted APT . By performing Monte Carlo simulations on several WS carpets we verify that plays the role of τ by setting the logarithmic period of the oscillatory asymptotic behaviour of dynamic observables.