Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

We generate jammed disordered packings of 100 <= N <= 2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting "polyrattlers" may be found imprisoned in shared cages as well as interacting through "bottlenecks" in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.