Generalized Langevin equation with fluctuating diffusivity

TL;DR

This paper introduces a generalized Langevin equation with fluctuating diffusivity (GLEFD), demonstrating its ability to model anomalous diffusion, non-Gaussian behavior, and relaxation phenomena, supported by analytical and numerical methods.

Contribution

It proposes the GLEFD framework, establishes its fluctuation-dissipation relation, and analyzes specific cases with power-law and exponential memory kernels.

Findings

GLEFD exhibits anomalous subdiffusion and non-Gaussianity with power-law kernels.

Analytical solutions show plateau structures in mean-square displacement.

A numerical scheme for GLEFD integration is developed.

Abstract

A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits anomalous subdiffusion, non-Gaussianity, and stretched-exponential relaxation. The case in which the memory kernel is given by a single exponential function is also investigated as an analytically tractable example. In particular, the mean-square displacement and the self-intermediate-scattering function of this system show plateau structures. A numerical scheme to integrate the GLEFD is also presented.