Disentangling sources of anomalous diffusion

TL;DR

This paper introduces a method to analyze subdiffusion by identifying a 'fundamental moment' that reveals the process's origin and properties, aiding in understanding complex anomalous diffusion behaviors.

Contribution

It proposes the concept of a 'fundamental moment' for assessing subdiffusion, linking process properties to underlying structural and energetic disorder components.

Findings

The fundamental moment's index is inherited from the parent process.

In disordered potential models, the index is determined by structural disorder.

Time dependence of the fundamental moment is influenced by energetic disorder.

Abstract

We show that some important properties of subbdiffusion of unknown origin (including those of mixed origin) can be easily assessed when findeng the "fundamental moment" of the corresponding process, i.e., the one which is additive in time. In subordinated processes, the index of the fundamental moment is inherited from the parent process and its time-dependence from the leading one. In models of particle's motion in disordered potentials, the index is governed by the structural part of the disorder while the time dependence is given by its energetic part.