Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations

TL;DR

This paper explores how equal-frequency double rotations can stabilize curved vortex surfaces in four-dimensional superfluids, extending understanding of topological excitations beyond lower dimensions.

Contribution

It demonstrates that certain curved vortex surfaces in 4D superfluids can be stabilized by equal-frequency double rotations, advancing the study of vortex phenomenology in higher dimensions.

Findings

Certain vortex surfaces are stabilized by double rotations.

The work extends vortex phenomenology to 4D superfluids.

Raises questions about vortex reconnections in higher dimensions.

Abstract

As is well-known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices respectively. Recently, we have studied how, in a hypothetical four-dimensional (4D) superfluid, such excitations can be generalised to vortex planes and surfaces. In this paper, we continue our analysis of skewed and curved vortex surfaces based on the 4D Gross-Pitaevskii equation, and show that certain types of such states can be stabilised by equal-frequency double rotations for suitable parameters. This work extends the rich phenomenology of vortex surfaces in 4D, and raises interesting questions about vortex reconnections and the competition between various vortex structures which have no direct analogue in lower dimensions.