NYU Physics Physics Colloquia

Ground-state problems naturally arise in many fields, including physics, biology, materials science, and mathematics. A classical ground-state configuration of a system of interacting particles is one that minimizes the system potential energy. In the laboratory, for example, such states can be produced by slowly cooling a liquid to a temperature of absolute zero, and usually the ground states are close-packed crystal structures. I will describe isotropic interactions with unusual crystal ground states in three dimensions (e.g., diamond lattice) as well as disordered ground states, a counterintuitive phenomenon. I then will discuss the problem of determining the densest packings of particles in Euclidean spaces, which are closely related to ground-state problems. We provide the putative exponential improvement on Minkowski's 100-year-old lower bound on the maximal packing density of spheres in high dimensions. This suggests that disordered (rather than ordered) sphere packings may be the densest for sufficiently large dimension, implying the existence of disordered ground states for some continuous potentials. Finally, I will describe a recent Kepler-like conjecture for the maximal-density packings of a majority of the Platonic and Archimedean solids.