Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

TL;DR

This paper derives an analytical fractional Fokker-Planck model for rotational relaxation in disordered systems, revealing non-exponential decay characterized by Mittag-Leffler functions, which aligns with experimental observations of complex relaxation behaviors.

Contribution

It introduces a fractional Fokker-Planck equation approach to analytically describe rotational relaxation in disordered systems, highlighting the non-exponential Kohlrausch-William-Watts law.

Findings

Rotational relaxation follows Mittag-Leffler decay.

Relaxation function exhibits fractional, non-exponential behavior.

Model aligns with complex disordered system dynamics.

Abstract

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.