Random walk on p-$adics in glassy systems

TL;DR

This paper demonstrates that p-adic analysis offers a natural framework for modeling relaxation processes in hierarchical glassy systems, leading to new insights into their decay behaviors.

Contribution

It introduces a p-adic random walk model for glassy relaxation, generalizing previous Cayley tree approaches and deriving temperature-dependent decay laws.

Findings

Derived power-law decay in relaxation dynamics.

Established Kohlrausch law within p-adic framework.

Connected p-adic analysis to hierarchical 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.