Abstract

The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms differs significantly from Brownian motion, manifest in a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. While such characteristic features have been extensively observed in experiments, there is so far no comprehensive theory explaining how they emerge from the microscopic active dynamics. Here we present a theoretical framework of the enhanced tracer diffusion in an active medium from its microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The tracer is shown to follow a non-Markovian coloured Poisson process that accounts quantitatively for all empirical observations [1]. The theory predicts in particular a long-lived Lévy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. Our framework provides the first validation of the celebrated Lévy flight model from a physical microscopic dynamics. With K. Kanazawa (University of Tsukuba), T. Sano (Keio University), and A. Cairoli (Crick Institute).[1] K. Kanazawa, T. Sano, A. Cairoli, A. Baule; Nature 579, 364 (2020)