First passage statistics for diffusing diffusivity

Abstract

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $⟨{\mathbf{r}}^2(t)⟩\simeq Dt$ yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a more efficient first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.

arXiv comment11 pages, 2 figures, IOP LaTeX

References in corpus (12)

• Anomalous transport in the crowded world of biological cells
• Superstatistics
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• A model of non-Gaussian diffusion in heterogeneous media
• Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
• Superstatistical Brownian motion
• First passage time statistics for two-channel diffusion
• Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics
• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles

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