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.

arXiv comment11 pages, 3 figures, 1 table

References in corpus (51)

• Anomalous transport in the crowded world of biological cells
• Superstatistics
• Lévy walks
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Dynamical foundations of nonextensive statistical mechanics
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Anomalous dynamics of cell migration
• Langevin equations for continuous time Lévy flights
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Anomalous diffusion in correlated continuous time random walks
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Scaled Brownian motion as a mean field model for continuous time random walks
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• Infinite Ergodic Theory for Heterogeneous Diffusion Processes
• Finite-time effects and ultraweak ergodicity breaking in superdiffusive dynamics
• Joint Probability Distributions for a Class of Non-Markovian Processes
• Time averaged Einstein relation and fluctuating diffusivities for the Lévy walk
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• The Lasting Effect of Initial Conditions on Single File Diffusion
• Quantifying the non-ergodicity of scaled Brownian motion
• Fractional kinetics emerging from ergodicity breaking in random media
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Superstatistical Brownian motion
• Tracer diffusion in a sea of polymers with binding zones: mobile vs frozen traps
• Comb model with slow and ultraslow diffusion
• From Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory
• Random time averaged diffusivities for Lévy walks
• The subdiffusive target problem: Survival probability
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• Continuous-time random-walk model for anomalous diffusion in expanding media
• Localization and ballistic diffusion for the tempered fractional Brownian-Langevin motion
• Enhancement, slow relaxation, ergodicity and rejuvenation of diffusion in biased continuous-time random walks
• Large deviations for continuous time random walks
• Lévy-walk-like Langevin dynamics
• Area coverage of radial Levy flights with periodic boundary conditions
• Subdiffusion in an external force field
• Ergodic properties of heterogeneous diffusion processes in a potential well
• Tempered fractional Langevin-Brownian motion with inverse $\beta$-stable subordinator
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Aging two-state process with Lévy walk and Brownian motion
• Langevin dynamics for Lévy walk with memory
• Lévy-walk-like Langevin dynamics affected by a time-dependent force

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