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.
Funder
Deutscher Akademischer Austauschdienst
National Natural Science Foundation of China
Deutsche Forschungsgemeinschaft
Chinese Council Scholarship
Fundacja na rzecz Nauki Polskiej
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
64 articles.
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