Influence of Dislocations in Thomson's Problem

TL;DR

This paper explores how dislocation defects influence the energy states of charges on a sphere in Thomson's problem, revealing that large systems favor less symmetric configurations with complex defect patterns.

Contribution

It demonstrates that for large numbers of charges, the lowest energy configurations are less symmetric and involve dislocation defects, extending understanding of defect patterns in spherical charge arrangements.

Findings

Large charge systems favor less symmetric states.

Dislocation defects screen strains from disclinations.

Complex defect patterns lower energy states.

Abstract

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.