Critical Scaling and Aging in Cooling Systems Near the Jamming Transition

We conduct athermal simulations of freely cooling, viscous soft spheres around the jamming transition density φJ and find evidence for a growing length ξ(t) that governs relaxation to mechanical equilibrium. ξ(t) is manifest in both the velocity correlation function and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities φ can be collapsed onto two master curves by scaling ξ(t) and t by powers of |φ-φJ|, indicative of critical scaling. Furthermore, particle transport for φ>φJ exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how ξ(t) at late times maps onto known behavior away from φJ.