Chiral Edge Modes in Helmholtz-Onsager Vortex Systems

TL;DR

This paper reveals that strongly interacting Helmholtz-Onsager vortex systems can form robust statistical edge modes at low energies, analogous to quantum Hall systems, with boundary dipoles confirmed through simulations and theory.

Contribution

It demonstrates the existence of edge modes in vortex systems, extending the analogy with quantum Hall effects and providing a theoretical and computational framework.

Findings

Edge modes form at low energies in vortex systems.

Dipoles of vortices and image vortices are associated with edge modes.

Edge modes persist in nonconvex domains and match mean-field predictions.

Abstract

Vortices play a fundamental role in the physics of two-dimensional (2D) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, point vortices in a 2D fluid continue to pose interesting theoretical problems, owing to their unusual statistical mechanics. Here, we show that the strongly interacting Helmholtz-Onsager vortex systems can form statistical edge modes at low energies, extending a previously identified analogy between vortex matter and quantum Hall systems. Through dynamical simulations, Monte-Carlo sampling and mean-field theory, we demonstrate that these edge modes are associated with the formation of dipoles of real and image vortices at boundaries. The edge modes are robust, persisting in nonconvex domains, and are in quantitative agreement with the mean-field predictions.