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arXiv · 1911.12195

Minimal energy point systems on the unit circle and the real line

Marcell Gaál·Béla Nagy·Zsuzsanna Nagy-Csiha·Szilárd Révész
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Abstract

In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of the discrete logarithmic energy are global minima, and they are the solutions of certain equations involving Blaschke products. As a nontrivial application, we refine a recent result of Simanek, namely, we prove that any configuration of $n$ electrons in the unit circle is in stable equilibrium (that is, they are not just critical points but are of minimal energy) with respect to an external field generated by $n-1$ pairs of protons.

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Marcell Gaál, Béla Nagy, Zsuzsanna Nagy-Csiha, Szilárd Révész. 2019-11-27. Minimal energy point systems on the unit circle and the real line. https://arxiv.org/abs/1911.12195

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