Subordination scenario of anomalous relaxation

TL;DR

This paper explains non-exponential relaxation phenomena using subordination by inverse tempered alpha-stable processes, linking empirical response functions with theoretical stochastic models and deriving a new relaxation function.

Contribution

It introduces a subordination framework with tempered alpha-stable processes to model anomalous relaxation, connecting empirical laws with stochastic process theory.

Findings

Derived the tempered relaxation function.

Linked Cole-Cole and Cole-Davidson response laws.

Clarified the empirical meaning of response functions.

Abstract

The non-exponential relaxation is shown to result from subordination by inverse tempered \alpha-stable processes. The main feature of tempered \alpha-stable processes is a finiteness of their moments, and the class of random processes includes ordinary \alpha-stable processes as a particular case. Starting with the Cole-Cole response this subordination approach establishes its direct link with the Cole-Davidson law. We derive the relaxation function describing the tempered relaxation. The meaning of the empirical response function is clarified.