Large-scale structure of randomly jammed particles

TL;DR

This study investigates the large-scale density fluctuations in randomly jammed particle packings, revealing they are not hyperuniform and exhibit complex, short-range correlations contrary to previous expectations.

Contribution

It provides a detailed numerical analysis of large-scale density fluctuations, demonstrating the absence of hyperuniformity and characterizing the complex structure of correlations in jammed packings.

Findings

Density fluctuations are not hyperuniform at large scales.

Pair correlation function shows complex large-distance structure.

Direct correlation function is short-ranged.

Abstract

We numerically analyse the density field of three-dimensional randomly jammed packings of monodisperse soft frictionles spherical particles, paying special attention to fluctuations occurring at large lengthscales. We study in detail the two-point static structure factor at low wavevectors in Fourier space. We also analyse 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.