Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises

TL;DR

This paper investigates anomalous diffusion phenomena in complex media using a generalized Langevin equation framework, analyzing various noise types and their effects on particle dynamics, including subdiffusion, superdiffusion, and ultraslow diffusion.

Contribution

It introduces a comprehensive analysis of anomalous diffusion driven by power-law-correlated and distributed-order noises within the generalized Langevin equation approach.

Findings

Derived MSD and correlation functions for different noise types.

Identified conditions for subdiffusion, superdiffusion, and ultraslow diffusion.

Showed models can describe complex diffusive behaviors in media.

Abstract

We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalized versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalized displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped generalized Langevin equations for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviors.