Topological Constraints on the Charge Distributions for the Thomson Problem

Details Topological Constraints on the Charge Distributions for the Thomson Problem Topological Constraints on the Charge Distributions for the Thomson Problem

2006-03-02

arxiv.org/abs/cond-mat/0603044v1

Physics

Condensed Matter

Other Condensed Matter

10 pages; dedicated to Rafael Sorkin on his 60th birthday

Scientific paper

10.1103/PhysRevB.74.052102

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.

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