Unexpected Density Fluctuations in Jammed Disordered Sphere Packings

TL;DR

This study investigates large-scale jammed disordered sphere packings, revealing they are hyperuniform with unique density fluctuation behaviors and unusual structural features like a linear structure factor dependence near zero.

Contribution

It demonstrates that large disordered sphere packings are hyperuniform and uncovers their distinctive density fluctuation and structural properties, including a non-analytic structure factor.

Findings

Packings are saturated and hyperuniform.

Local density fluctuations grow logarithmically with surface area.

Structure factor exhibits a linear dependence near zero.

Abstract

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 non-analytic linear dependence near the origin, $S(k)\sim|k|$. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, $h(r)\sim-r^{-4}$, and a long-ranged direct correlation function.