The Spectrum of Structure for Jammed and Unjammed Soft Disks

TL;DR

This paper explores the structural properties of soft disk configurations near jamming, revealing how fluctuations and hyperuniformity vary with system parameters and protocols, using a real-space spectral approach.

Contribution

It introduces a real-space spectrum of hyperuniformity lengths to analyze structural features of jammed and unjammed soft disks, providing clearer insights than traditional spectral density methods.

Findings

Unjammed configurations show size-dependent super-Poissonian long-range features.

Near jamming, spectra exhibit a protocol-independent plateau indicating hyperuniformity.

Real-space hyperuniformity lengths offer more intuitive structural insights than spectral density.

Abstract

We investigate the short, medium, and long-range structure of soft disk configurations for a wide range of area fractions and simulation protocols by converting the real-space spectrum of volume fraction fluctuations for windows of width $L$ to the distance $h(L)$ from the window boundary over which fluctuations occur. Rapidly quenched unjammed configurations exhibit size-dependent super-Poissonian long-range features that, surprisingly, approach the totally-random limit even close to jamming. Above and just below jamming, the spectra exhibit a plateau, $h(L)=h_e$, for $L$ larger than particle size and smaller than a cutoff $L_c$ beyond which there are long-range fluctuations. The value of $h_e$ is independent of protocol and characterizes the putative hyperuniform limit. This behavior is compared with that for Einstein solids, with and without hyperuniformity-destroying defects. We find that key structural features of the particle configurations are more evident, as well as easier and more intuitive to quantify, using the real-space spectrum of hyperuniformity lengths rather than the spectral density.