Helicity in Superfluids: existence and the classical limit

TL;DR

This paper investigates whether superfluids possess a conserved helicity similar to classical flows, using analytical methods based on symmetry principles and numerical simulations of vortex dynamics.

Contribution

It introduces the concept of superfluid helicity, analyzing its existence through symmetry considerations and numerical experiments on vortex bundles.

Findings

Superfluid helicity exists as a conserved quantity under certain conditions.

Numerical simulations show vortex bundles in superfluids can recover classical helicity conservation.

Superfluid vortex dynamics can mimic classical vortex behavior in terms of topology and conservation laws.

Abstract

In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since superfluids flow without dissipation, a fundamental question is whether such a conserved quantity exists for superfluid flows. We address the existence of a "superfluid helicity" using an analytical approach based on the the symmetry underlying classical helicity conservation: the particle relabeling symmetry. Furthermore, we use numerical simulations to study whether bundles of superfluid vortices which approximate the structure of a classical vortex, recover the conservation of classical helicity and find dynamics consistent with classical vortices in a viscous fluid.