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arXiv · 1804.04927

Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity

M. J. Godfrey·M. A. Moore
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Abstract

We relate the structure factor $S(\mathbf{k} \to \mathbf{0})$ in a system of jammed hard spheres of number density $ρ$ to its complexity per particle $Σ(ρ)$ by the formula $S(\mathbf{k} \to \mathbf{0})=-1/ [ρ^2Σ''(ρ)+2ρΣ'(ρ)]$. We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find $Σ(ρ)$ and $S(\mathbf{k})$ analytically. Hyperuniformity, which is the vanishing of $S(\mathbf{k} \to \mathbf{0})$, will therefore not occur if the complexity is nonzero. An example is given of a jammed state of hard disks in a narrow channel which is hyperuniform when generated by dynamical rules that produce a non-extensive complexity.

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M. J. Godfrey, M. A. Moore. 2018-08-20. Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity. https://doi.org/10.1103/physrevlett.121.075503

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