Hausdorff dimension and hierarchical system dynamics

TL;DR

This paper demonstrates that Hausdorff dimension can differentiate various relaxation dynamics in hierarchical systems, using p-adic Lévy processes to analyze temperature-dependent decay laws.

Contribution

It introduces a novel application of Hausdorff dimension to distinguish relaxation behaviors in hierarchical systems via p-adic stochastic processes.

Findings

Hausdorff dimension differentiates relaxation dynamics

Analysis of power-law and Kohlrausch decay laws

Application of p-adic Lévy processes

Abstract

We show that Hausdorff dimension may be used to distinguish different dynamics of therelaxation in hierarchical systems. We examine the hierarchical systems following the temperature-dependent power-law decay and the Kohlrausch law. For our purposes, we consider a L\'evy stochastic processes on p-adic integer numbers.