Anomalous relaxation in regular and fractal lattices

Abstract

Relaxation phenomena on disordered structures are studied by using a random walk model. The model is able to describe essential features of the relaxation process in terms of a one-body picture with geometrical restrictions on the particles' motion. Two cases are considered: relaxation on regular lattices with disordered variables taken from a power-law distribution (these variables have different updating rules), and on a fractal lattice which is a percolation cluster near criticality. Quantities such as the relaxation function, particle density, and complex susceptibility are evaluated. Different types of relaxation mechanisms are found as a function of frequency for regular and fractal lattices. Also for a regular lattice, we see an interesting dependence of the relaxation quantities as a function of a disorder parameter which describes the decay of the power-law distribution from which variables are drawn. The model is able to reproduce the relaxation behavior commonly observed in experiments and typically fitted to empirical laws.