Structure and dynamics of spherical crystals characterized for the Thomson problem

Candidates for global minima of the Thomson problem for N charges on a sphere are located for N≤400 and selected sizes up to $N=972$. These results supersede many of the lowest minima located in previous work, with particularly large improvements for $N>400$. Our analysis reveals interesting topological defects, which are likely to play an important role in determining the mechanical and electrical properties of systems confined to a spherical geometry. We also find low-energy rearrangements for the Thomson model, an observation which suggests that suitable mesoscopic systems with analogous coarse-grained structure may exhibit fluxional dynamics.