Abstract
We analyze the large scale structure and fluctuations of jammed packings of polydisperse spheres produced both numerically and in a granular experiment. While the structure factors of the packings reveal no unusual behavior for small wavevectors, the compressibility displays an anomalous linear dependence at low wavectors and vanishes when q -> 0. Our results apply to arbitrary particle size distributions. For continuous distributions, we derive simple perturbative approximations for the compressibility that are accurate for polydispersity up to about 30%. We show that the compressibility vanishes because jammed packings of polydisperse spheres have no bulk fluctuations of the volume fraction and are thus hyperuniform, a property not observed experimentally before.