Unexpected density fluctuations in jammed disordered sphere packings

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k)similar to vertical bar k vertical bar. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r)similar to-r(-4), and a long-ranged direct correlation function c(r).