Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass

The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom associated with contact dynamics control the appearance of macroscopic rigidity. We provide decisive experimental evidence that this transition is a critical phenomenon, with increasingly collective and heterogeneous rearrangements occurring at length scales much smaller than the grain diameter, presumably reflecting the contact force network fluctuations. Dynamical correlation time and length scales soar on both sides of the transition, as the volume fraction varies over a remarkably tiny range ($\delta \phi /\phi \sim 10^{- 3}$). We characterize the motion of individual grains, which becomes super-diffusive at the jamming transition $\phi _{J}$, signaling long-ranged temporal correlations. Correspondingly, the system exhibits long-ranged four-point dynamical correlations in space that obey critical scaling at the transition density