Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

TL;DR

This paper explores the properties of stealthy hyperuniform point patterns across multiple dimensions, confirming that the densest Fourier-space hard-sphere system is a Bravais lattice and extending predictions of spatial decorrelation.

Contribution

It demonstrates that the densest Fourier-space hard-sphere system is a Bravais lattice and extends virial series predictions to higher dimensions for disordered stealthy hyperuniform systems.

Findings

Densest Fourier-space hard-sphere system is a Bravais lattice.

Virial series extended to dimensions 2-8.

Numerical simulations confirm predictions of spatial decorrelation.

Abstract

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions $d=2$-$8$.