Normal and anomalous diffusion in the disordered wind-tree model

Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities $\rho$ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient $D$, as obtained from the simulation, with that predicted by kinetic theory where $D^{-1}$ is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times $t$ grows like $t^{1-2\rho /3}$. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.