Fractional Brownian motion with fluctuating diffusivities

TL;DR

This paper introduces a generalized fractional Brownian motion model with stochastic diffusivity, providing analytical tools and validation for systems with heterogeneities in tracers or environment, advancing the understanding of anomalous diffusion.

Contribution

It develops a new framework for fractional Brownian motion with fluctuating diffusivities, extending previous models to better capture heterogeneities in complex systems.

Findings

Derived analytical autocovariance and mean squared displacement expressions.

Validated the model with numerical simulations of two-state systems.

Demonstrated the framework's effectiveness in describing heterogeneous diffusion.

Abstract

Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach of a generalization that incorporates heterogeneities in either the tracers or the environment. This work presents a modification of Levy's representation of fBm for the case in which the generalized diffusion coefficient is a stochastic process. We derive analytical expressions for the autocovariance function and both ensemble- and time-averaged mean squared displacements. Further, we validate the efficacy of the developed framework in two-state systems, comparing analytical asymptotic expressions with numerical simulations.