The necessity of choice in hard sphere jamming algorithms

Jamming occurs upon compression of a system of hard particles until the emergence of bulk or shear modulus. Absent explicit thermalization along that compression, the state thus obtained is expected to correspond to the inherent state of the initial (fluid) configuration. Yet each compression scheme results in a distinct end point, suggesting a persistent (implicit) thermalization. To fully exclude such effects, we here consider an overdamped dynamics, under which the system evolves by oscillating between two intermittent states: 1) a network of contacting particles which remains intact throughout expansion until a new contact is formed; and 2) a network which is incompatible insofar as the dynamics forces an overlap upon infinitesimal expansion unless a bond is broken. Until recently, it was assumed that only one compatible state could be created by bond removal in the second state, but a study of jamming in the random Lorentz gas has revealed otherwise. Several such states can in fact be created, thus significantly affecting the jammed state eventually reached. Applying this logic to traditional hard spheres uncovers a tree of jammed states obtained from a same starting configuration, upon following different bond removal schemes. By ordering the choices of bond removal by the amount of free volume that they make available, we hope to unambiguously identify the true inherent state of a given hard sphere fluid.