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

Nils-Eric Guenther; Pietro Massignan; Alexander L. Fetter

doi:10.1103/physreva.101.053606

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arXiv · 1911.11794

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

Nils-Eric Guenther·Pietro Massignan·Alexander L. Fetter

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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.

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Nils-Eric Guenther, Pietro Massignan, Alexander L. Fetter. 2019-11-26. Superfluid vortex dynamics on a torus and other toroidal surfaces of revolution. https://doi.org/10.1103/physreva.101.053606

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