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Charge distribution in two-dimensional electrostatics

I. Kogan·A. M. Perelomov·G. W. Semenoff
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Abstract

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.

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I. Kogan, A. M. Perelomov, G. W. Semenoff. 2002-05-25. Charge distribution in two-dimensional electrostatics. https://doi.org/10.1103/physrevb.45.12084

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