Volume distribution in high-dimensional energy landscapes

Disordered packings of monodisperse, jammed repulsive soft spheres in 3D exist within a rugged potential-energy landscape where each basin's local minimum corresponds to a mechanically stable configuration. The volume of each basin is measured as the probability of reaching its corresponding local minimum from an initial configuration with random particle positions. By ranking these basin volumes from largest (n=1) to smallest, we observe that their volumes approximately follow: V(n)∝1/n. This holds for at least 70% of the total volume of the energy landscape for systems up to N=79. Even for N ≤ 151, the power-law regime contains at least 10% of the total volume. These limits are determined only by computational power. This suggests that this relation describes an even larger portion of the energy landscape. The structure observed in the statistics of the basin volumes is likely to have important implications for the dynamics of glassy systems and how jammed systems respond to perturbations.