Edge modes of the Helmholtz-Onsager gas in a multiply-connected domain

TL;DR

This paper explores the behavior of vortex gases in multiply-connected domains, revealing the existence of edge modes at low energy states through various sampling and mean field methods.

Contribution

It introduces evidence for edge modes in vortex gases on annular domains using mean field theory and sampling techniques, advancing understanding of 2D flow in complex geometries.

Findings

Edge modes are present at low energy states.

Multiple sampling methods confirm edge mode existence.

The study enhances understanding of vortex behavior in multiply-connected domains.

Abstract

The vortex gas is an approximation used to study 2D flow using statistical mechanics methodologies. We investigate low positive Onsager temperature states for the vortex gas on an annular domain. Using mean field theory, microcanonical sampling of the point gas model, and canonical sampling of a lattice model, we find evidence for edge modes at low energy states.