The geometry of jamming algorithms in the random Lorentz gas

Deterministic optimization algorithms unequivocally partition a complex energy landscape into inherent structures (ISs) and their respective basins of attraction. Can these basins be defined solely through geometric principles? This question is paramount to understanding hard sphere jamming, a key model of disordered matter. We here address the issue by proposing a geometric class of gradient descent-like algorithms, which we use to study a system in the hard-sphere universality class, the random Lorentz gas. The statistics of the resulting ISs is found to be strictly inherited from those of Poisson-Voronoi tessellations. The landscape roughness is further found to give rise to a hierarchical organization of ISs, which various algorithms explore differently. In particular, greedy and reluctant schemes tend to favor ISs of markedly different densities. The resulting ISs nevertheless robustly exhibit a universal force distribution, thus confirming the geometric nature of the jamming universality class. Along the way, the physical origin of a dynamical Gardner transition is identified.