One-component plasma on a spherical annulus and a random matrix ensemble

TL;DR

This paper investigates the two-dimensional one-component plasma at  on a spherical annulus, analyzing its asymptotic properties and connecting it to a specific random matrix ensemble derived from complex Gaussian and Haar unitary matrices.

Contribution

It extends the understanding of the  plasma to spherical annuli with soft walls and links it to a novel random matrix ensemble via stereographic projection.

Findings

Derived asymptotic forms of the plasma on a spherical annulus.

Established a connection between the plasma system and a random matrix ensemble.

Analyzed boundary effects and general properties of the plasma.

Abstract

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.