First passage statistics for diffusing diffusivity

TL;DR

This paper analyzes the first passage behavior of the diffusing diffusivity model, revealing significant deviations from classical Brownian motion and identifying a universal crossover in survival probability.

Contribution

It provides analytical and numerical insights into the first passage statistics of the DD model, highlighting its distinct dynamics and universal features.

Findings

DD model shows more efficient first passage dynamics than Brownian motion

Universal crossover point in survival probability independent of initial conditions

Significant modifications in first passage behavior due to stochastic diffusivity

Abstract

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ 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.