Classical Many-particle Clusters in Two Dimensions

Abstract

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction but dependent only on its functional form. It is also independent of the magnetic field strength when included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally we report some interesting results when a three-body interaction is included, albeit in a particular model.

Minor corrections, a few references added. To appear in J. Phys: Condensed Matter

References in corpus (5)

• Classical artificial two-dimensional atoms: the Thomson model
• Analytic results for $N$ particles with $1/r^2$ interaction in two dimensions and an external magnetic field
• A Quantum Many-body Problem in Two Dimensions: Ground State
• Classical Dynamics of Anyons and the Quantum Spectrum
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