Solitons in finite droplets of noncommutative Maxwell-Chern-Simons theory

TL;DR

This paper discovers exact and new soliton solutions in a finite noncommutative Maxwell-Chern-Simons model, directly related to quantum Hall physics, and computes their fluxes and energies.

Contribution

It provides explicit soliton solutions in a finite droplet setting of the noncommutative Maxwell-Chern-Simons theory, extending previous hypotheses and models.

Findings

Exact soliton solutions confirmed in finite droplets

New variations of solitons identified

Computed fluxes and energies of the solitons

Abstract

We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their flux and their energies. The model we consider is directly related to the model proposed by Polychronakos\cite{Poly} and studied by Hellerman and Van Raamsdonk\cite{HvR} where it was shown that it is equivalent to the quantum Hall effect.