Anomalous diffusion in polydisperse granular gases

We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system in a homogeneous cooling state and derive rigorous analytical expressions valid both at short and long time scales. The discrepancies in ensemble and time-averaged mean-squared displacements indicate ergodicity breaking in granular systems consisting of an arbitrary number of species of different sizes and masses. We compare the results of our study with Monte Carlo simulations in terms of a powerful low-rank algorithm and find a nice agreement.