Large-scale structure of randomly jammed spheres

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.