Ergodic property of random diffusivity system with trapping events

Abstract

Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an $\alpha$-stable subordinator with $\alpha <1$. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble- and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model for any kind of diffusivity, including the critical case where the model presenting normal diffusion.

11 pages, 3 figures, 1 table

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Cited by in corpus (4)

• Langevin picture of anomalous diffusion processes in expanding medium
• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Random diffusivity processes in an external force field
• Non-normalizable quasi-equilibrium states under fractional dynamics