Superfluid Vortex Dynamics on Planar Sectors and Cones

Abstract

We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the straight sides. The sector can then be mapped conformally to the whole plane, leading to the relevant stream function. In this way, we show that a superfluid vortex on the cone precesses uniformly at fixed distance from the apex. The stream function also yields directly the interaction energy of two vortices on the cone. We then study the vortex dynamics on unbounded and bounded cones. In suitable limits, we recover the known results for dynamics on cylinders and planar annuli.

10 pages, 8 figures

References in corpus (8)

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• Synthetic Landau levels for photons
• Vortices in Superfluid Films on Curved Surfaces
• Anomalous coupling between topological defects and curvature
• Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli
• Layering transitions in superfluid helium adsorbed on a carbon nanotube mechanical resonator
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Cited by in corpus (8)

• Low-dimensional quantum gases in curved geometries
• Bose-Einstein Condensation on Curved Manifolds
• Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution
• Superfluid vortex dynamics on a spherical film
• Superfluid vortex dynamics on a torus and other toroidal surfaces of revolution
• Quantum Vortices in Curved Geometries
• Superfluid vortex multipoles and soliton stripes on a torus
• Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary