Slow timescales in out of equilibrium systems: the case of vibrofluidized granular matter

We address the problem of emerging slow timescales in the context of non-equilibrium athermal systems through the study of vibrofluidized granular materials. Recent experimental results for a tracer immersed in a dense vibrated granular fluid revealed an unexpected superdiffusive behaviour at large times. We perform a numerical study based on the discrete element method that clarifies the origin of this memory effect unveiling a slow collective motion of the granular medium. Two different modelling approaches are then followed. The first one is a phenomenological theory aiming at reproducing the experimental and numerical results of the previous studies; the second one consists of a lattice model to explain the emergence of long-range correlations and slow timescales in a driven granular system. Finally, an extensive analysis of a simplified numerical setup sheds light on the crucial relationship between the transient symmetry breaking induced by disorder in the granular medium and its slow collective motion. We also provide some insights into fast timescales considering the problem of energy transfer to a dense vibrated granular system