p-Adic description of characteristic relaxation in complex systems

TL;DR

This paper uses p-adic analysis to model relaxation processes in complex systems, revealing that different decay laws are similar ultrametric processes governed by a hierarchical energy landscape.

Contribution

It develops a p-adic framework to describe various relaxation laws as ultrametric processes, linking them to hierarchical energy landscapes.

Findings

Relaxation processes are modeled as ultrametric random walks.

Different decay laws are shown to be similar processes.

The p-adic master equation describes the relaxation dynamics.

Abstract

This work is a further development of an approach to the description of relaxation processes in complex systems on the basis of the p-adic analysis. We show that three types of relaxation fitted into the Kohlrausch-Williams-Watts law, the power decay law, or the logarithmic decay law, are similar random processes. Inherently, these processes are ultrametric and are described by the p-adic master equation. The physical meaning of this equation is explained in terms of a random walk constrained by a hierarchical energy landscape. We also discuss relations between the relaxation kinetics and the energy landscapes.