Long-Range Anomalous Decay of the Correlation in Jammed Packings

TL;DR

This study investigates the large-scale structure and correlations in three-dimensional jammed packings of hard spheres, revealing anomalous long-range decay and complex oscillatory behavior in density correlations.

Contribution

It introduces a correlation function based on density fluctuations and contact points to analyze weak forces and coordination number variations in jammed packings, supporting hyperuniformity.

Findings

Evidence of anomalous long-range decay in correlations.

Complex superposition of oscillating signals in density correlations.

Support for hyperuniformity in randomly jammed packings.

Abstract

We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number with respect to the isostaticity condition $\Delta Z$. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the $\Delta Z$ fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies.