Superfluid vortex dynamics on a torus and other toroidal surfaces of revolution

TL;DR

This paper analyzes superfluid vortex dynamics on a torus and other revolution surfaces, deriving analytic expressions for flow, energy, and vortex motion, highlighting the effects of curvature and topology.

Contribution

It provides new analytic models for vortex behavior on toroidal surfaces, considering curvature and topology effects, which were not previously detailed.

Findings

Flow and energy expressions derived for superfluid vortices on a torus

Curvature and topology significantly influence vortex dynamics

Vortex configurations constrained by zero net vorticity on compact surfaces

Abstract

The superfluid flow velocity is proportional to the gradient of the phase of the superfluid order parameter, leading to the quantization of circulation around a vortex core. In this work, we study the dynamics of a superfluid film on the surface of a torus. Such a compact surface allows only configurations of vortices with zero net vorticity. We derive analytic expressions for the flow field, the total energy, and the time-dependent dynamics of the vortex cores. The local curvature of the torus and the presence of non-contractable loops on this multiply connected surface alter both the superfluid flow and the vortex dynamics. Finally we consider more general surfaces of revolution, called toroids.