Rotation of quantum liquid without singular vortex lines

TL;DR

This paper explores a quantum hydrodynamics solution in cylindrical geometry where the velocity curl is embedded in the density without singular vortices, analyzing its oscillation spectrum and stability.

Contribution

It introduces a novel vortex-free quantum hydrodynamics solution with a generalized phonon spectrum and demonstrates its stability.

Findings

Velocity curl is 'frozen' into the density without singular vortices.

Derived the spectrum of small oscillations around the solution.

Proved the stability of the vortex-free solution.

Abstract

The operator equations for quantum hydrodynamics are discussed and solved in a simple cylindrical geometry. We find a solution with the velocity curl "frozen" into a density of the liquid in the absence of singular vortex lines. The spectrum of small oscillations around this solution is found as a generalization of the standard phonon spectrum, and the stability of the solution is demonstrated.