Gaál, Marcell Gábor and Nagy, Béla and Nagy-Csiha, Zsuzsanna and Révész, Szilárd (2020) Minimal Energy Point Systems on the Unit Circle and the Real Line. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52 (6). pp. 6281-6296. ISSN 0036-1410
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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.
Item Type: | Article |
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Uncontrolled Keywords: | Potential theory; External fields; electrostatic equilibrium; Blaschke product; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 10 Feb 2023 08:26 |
Last Modified: | 10 Feb 2023 08:26 |
URI: | http://real.mtak.hu/id/eprint/158694 |
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