Topological Constraints on the Charge Distributions for the Thomson Problem
arXiv:cond-mat/0603044 · doi:10.1103/PhysRevB.74.052102
Abstract
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the system may organize itself in the form of pentagonal structures. This gives a qualitative account for the interesting ``pentagonal buttons'' discovered in recent numerical work.
10 pages; dedicated to Rafael Sorkin on his 60th birthday