Random walk on p-$adics in glassy systems

Abstract

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical glassy systems. For our purposes, we specify the Markov stochastic process considered by S. Albeverio and W. Karwowski. As a result we have obtained a random walk on p-adic integer numbers, which provide the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.