Time-averaged MSD for switching diffusion

Abstract

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e., the trajectory duration) is comparable to or smaller than the mean residence times in each state, the ergodicity breaking parameter is shown to take arbitrarily large values, suggesting an apparent weak ergodicity breaking for this ergodic model. In this regime, individual random trajectories are not representative while the related TAMSD curves exhibit a broad spread, in agreement with experimental observations in living cells and complex fluids. Switching diffusions can thus present, in some cases, an ergodic alternative to commonly used and inherently non-ergodic continuous-time random walks that capture similar features.

References in corpus (12)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Diffusion-limited reactions in dynamic heterogeneous media
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• A model of non-Gaussian diffusion in heterogeneous media
• First passage statistics for diffusing diffusivity
• First passage time statistics for two-channel diffusion
• Unravelling intermittent features in single particle trajectories by a local convex hull method
• Kinetics of active surface-mediated diffusion in spherically symmetric domains
• Exact mean exit time for surface-mediated diffusion
• The Kärger vs bi-exponential model: theoretical insights and experimental validations

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