**Spectrum of structure for jammed and unjammed soft disks**

AT Chieco and M Zu and AJ Liu and N Xu and DJ Durian, PHYSICAL REVIEW E, 98, 042606 (2018).

DOI: 10.1103/PhysRevE.98.042606

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 he 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.

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