Direct Measurements of the Complexity of the Sphere Packing Energy Landscape*

Granular systems have complex and high dimensional potential energy landscapes. By directly characterizing this landscape we can gain statistical insight into material properties. We approximate this landscape as that of frictionless spheres and characterize their energy landscape by enumerating the local minima found within randomly chosen small volumes. Inspired by the mark-recapture method often used in estimation of populations, we repeatedly minimize a family of slightly perturbed harmonic soft sphere packings to determine the density and sizes of the minima found within that volume. We report on the complexity and statistical properties of the energy landscape as a function of the distance from jamming and comment on the relation to the theorized Gardner transition in jamming.