Gaál, Marcell Gábor and Nagy, Béla and NagyCsiha, 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. 62816296. ISSN 00361410

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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 

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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