Year: 2017
Type: article
Abstract: Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}/(2MR)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\ensuremath{\chi}({\mathbit{r}}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\mathbit{r}}_{12}$ becomes larger than the cylinder radius. An appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.
Source: Physical Review A
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2750656937