Long-Range Anomalous Decay of the Correlation in 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.

arXiv commentMain: 5 pages, 4 figures; Supp. Info.: 2 pages, 1 figure

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• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Random Close Packing of Semi-Flexible Polymers in Two Dimensions: Emergence of Local and Global Order
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores
• Generic power laws in higher-dimensional lattice models with multidirectional hopping
• Hyperuniformity near jamming transition over a wide range of bidispersity
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media