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Topological Constraints on the Charge Distributions for the Thomson Problem

Alfredo Iorio·Siddhartha Sen
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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.

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Alfredo Iorio, Siddhartha Sen. 2006-03-02. Topological Constraints on the Charge Distributions for the Thomson Problem. https://doi.org/10.1103/physrevb.74.052102

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