סמינר לפיזיקה של מערכות ביולוגיות וחומרים רכים: Brownian yet non-Gaussian Diffusion

Abstract:

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. To explain such behavior we introduce and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the "diffusing diffusivity" process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations. We also discuss the situations under which Brownian yet non-Gaussian diffusion can be observed in the model of a particle’s motion in a random landscape of diffusion coefficients slowly varying in space.