Distributional Behaviors of Time-averaged Observables in Langevin Equation with Fluctuating Diffusivity: Normal Diffusion but Anomalous Fluctuations

TL;DR

This paper analyzes a Langevin equation with fluctuating diffusivity, revealing that despite normal diffusion, the fluctuations of time-averaged observables are anomalous due to diverging sojourn times, relevant for single-particle tracking.

Contribution

It introduces a model with dichotomously fluctuating diffusivity and demonstrates how it causes anomalous fluctuations in time-averaged diffusivity, even under normal diffusion conditions.

Findings

Occupation time statistics effectively compute time-averaged MSD.

Time-averaged diffusion coefficients are inherently random with diverging sojourn times.

The model explains large fluctuations observed in single-particle tracking experiments.

Abstract

We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion process. We find that occupation time statistics is a powerful tool for calculating the time-averaged mean square displacement in the model. We show that the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges. Our model provides anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficient in single-particle-tracking experiments.