Low density sphere packings derived from stealthy hyperuniform point patterns

Stealthy hyperuniform point patterns are characterized by a structure factor S(k) which is identically zero for a range of wavevectors 0<|k|<K. Generating these patterns numerically involves the minimization of an objective function Φ that is proportional to a weighted sum of S(k) over the interval 0<|k|<K. Whenever a global minimum (Φ=0) is obtained, the system is thus automatically stealthy hyperuniform. Recent work has shown that by adding a soft-core repulsive term to Φ with a given contact distance σ, one can create point patterns that are both stealthy hyperuniform and that form the basis for hard spheres with diameter σ. By increasing σ, one can even create jammed packings. However, without the soft-core repulsion, nothing prevents points from becoming arbitrarily close. In this talk, we investigate the maximum density hard sphere packing that can be embedded on stealthy hyperuniform patterns generated without soft-core repulsion as a function of the system size, spatial dimension, and size of the stealthy exclusion region K. While the packing fraction goes to zero in the limit of large system sizes as expected, the functional form of the system size dependence reveals key insights into the landscape of stealthy hyperuniform configurations.