Classical Many-particle Clusters in Two Dimensions

TL;DR

This paper investigates the equilibrium configurations and shell structures of classical particles confined in two dimensions, analyzing effects of interaction, confinement potential, and three-body interactions, with analytical and theoretical insights.

Contribution

Develops an analytical method for equilibrium configurations and explores how shell structures depend on interaction form and confinement, including effects of three-body interactions.

Findings

Shell transition from 5 to 6 particles in harmonic confinement

Shell structure depends only on interaction form, not strength or magnetic field

Three-body interactions influence equilibrium configurations

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.