Ergodicity recovery of random walk in heterogeneous disordered media

Abstract

Significant and persistent trajectory-to-trajectory variance are commonly observed in the particle tracking experiments, which have become a major challenge for the experiment data analysis. In this theoretical paper, we investigate the ergodicity recovery behavior, which helps to clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media. The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis. The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations. The strange ergodicity recovery behavior is reported in the quenched disordered case, which arises from a localization mechanism. The first-passage approach is introduced to the ergodicity analysis for this case, of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.

arXiv comment9 pages, 7 figures

References in corpus (13)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Granular materials flow like complex fluids
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Anomalous dynamics of intruders in a crowded environment of mobile obstacles
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Observation of electroweak production of a same-sign $W$ boson pair in association with two jets in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Non-Gaussian diffusion in static disordered media
• Quenched trap model on the extreme landscape: the rise of sub-diffusion and non-Gaussian diffusion
• Sample-dependent first-passage time distribution in a disordered medium