Two-dimensional one-component plasma in a quadrupolar field

TL;DR

This paper analyzes a two-dimensional one-component plasma with a quadrupolar potential, confirming particle distribution and correlation properties through microscopic and macroscopic approaches, revealing universal surface charge correlations.

Contribution

It provides a microscopic calculation of surface charge correlations in a 2D plasma with quadrupolar potential, extending previous work and confirming universal behavior.

Findings

Particles form an elliptical distribution in the plasma.

Surface charge correlation function exhibits universal form.

Microscopic and macroscopic approaches agree on particle distribution.

Abstract

The classical two-dimensional one-component plasma is an exactly solvable model, at some special temperature, even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco, Gaudin, Itzykson, and Lesage [{\it Int. J. Mod. Phys.} {\bf A9}, 4257 (1994)] about an $N$-particle system ($N$ large but finite), a macroscopic argument is given for confirming that the particles form an elliptical blob, the analogy between the classical plasma and a quantum $N$-fermion system in a magnetic field is used for the microscopic approach, and a microscopic calculation of the surface charge-surface charge correlation function is performed; an expected universal form is shown to be realized by this correlation function.