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

Abstract

We relate the structure factor $S(\mathbf{k}\to 0)$ in a system of jammed hard spheres of number density $\rho$ to its complexity per particle $\Sigma (\rho )$ by the formula $S(\mathbf{k}\to 0)=-1/[{\rho }^2{\Sigma }^{\prime \prime }(\rho )+2\rho {\Sigma }^{\prime }(\rho )]$. We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find $\Sigma (\rho )$ and $S(\mathbf{k})$ analytically. Hyperuniformity, which is the vanishing of $S(\mathbf{k}\to 0)$, 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.

5 pages, 3 figures