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

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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Cited by in corpus (11)

• Vortex-antivortex physics in shell-shaped Bose-Einstein condensates
• Low-dimensional quantum gases in curved geometries
• Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution
• Superfluid vortex dynamics on a spherical film
• Quantum Vortices in Curved Geometries
• Engineering phase and density of Bose-Einstein condensates in curved waveguides with toroidal topology
• Superfluid excitations in rotating two-dimensional ring traps
• Superfluid vortex multipoles and soliton stripes on a torus
• Dynamics of Vortex Clusters on a Torus
• Synthetic half-integer magnetic monopole and single-vortex dynamics in spherical Bose-Einstein condensates
• Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary