Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. (4th November 2020)

• Record Type: Journal Article
• Authors: Wang, Wei; Cherstvy, Andrey G; Chechkin, Aleksei V; Thapa, Samudrajit; Seno, Flavio; Liu, Xianbin; Metzler, Ralf
• Is Part Of: Journal of physics. Volume 53:Number 47(2020)
• Publication Date: 2020-11-04
• Subjects: stochastic processes -- anomalous diffusion -- fractional Brownian motion -- diffusing diffusivity -- weak ergodicity breaking; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aba467
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time τ characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on τ and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.