Critical slowing down and hyperuniformity on approach to jamming

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004), 10.1016/j.jcp.2003.11.022] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called "pressure-leak" test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N ≈10³ bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of "critical slowing down" as the packing's collective rearrangements in configuration space become locally confined by high-dimensional "bottlenecks" from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler free, which is an outstanding, challenging task.