Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packing

We track the motion of a horizontally vibrated amorphous assembly of bidisperse hard disks, for densities ranging across the jamming transition. We derive on very general grounds a bound on the dynamical susceptibility in terms of the response of the dynamics to a change in density. This generalizes a similar bound recently derived for equilibrium liquids. We find that in our experimental system the bound is tight and reproduces the non-monotonic behavior of the dynamical susceptibility both in time and density across the jamming transition. The underlying scaling behavior reveals an intimate connection between anomalous diffusion and dynamical heterogeneity. Copyright (c) EPLA, 2008.