A Solvable Mixed Charge Ensemble on the Line: Global Results

TL;DR

This paper analyzes a solvable model of two-species charged particles on a line under harmonic confinement, revealing their distribution and density in the large charge limit through Pfaffian point process techniques.

Contribution

It introduces a new exactly solvable model with mixed charges on the line and derives the associated Pfaffian point process structure and skew-orthogonal polynomials.

Findings

Distribution of particle numbers and densities in the large charge limit

Explicit construction of skew-orthogonal polynomials for the model

Identification of the Pfaffian point process structure

Abstract

We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2 : 1 in the presence of the harmonic oscillator potential. The system is assumed to be at temperature corresponding to \beta = 1 and the sum of the charges is fixed. We investigate the distribution of the number as well as the spatial density of each species of particle in the limit as the total charge increases to \infty. These results will follow from the fact that the system of particles forms a Pfaffian point process. We produce the skew-orthogonal polynomials necessary to simplify the related matrix kernels.