Nonrelativistic Chern-Simons Vortices on the Torus

TL;DR

This paper classifies all periodic self-dual vortex solutions in the Jackiw-Pi model on a torus, introduces a new class of functions called Omega-quasi-elliptic, and explores phenomena like vortex charge loss in the planar limit.

Contribution

It provides a comprehensive classification of vortex solutions on the torus and introduces the novel Omega-quasi-elliptic functions related to these solutions.

Findings

Classification of all periodic self-dual vortex solutions.

Introduction of Omega-quasi-elliptic functions.

Observation of vortex charge loss in the planar limit.

Abstract

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.