Helicity conservation under quantum reconnection of vortex rings

TL;DR

This paper demonstrates that in quantum vortex reconnections modeled by the Gross-Pitaevskii equation, the self-helicity of vortex rings remains conserved, with detailed analysis of their geometric and topological properties.

Contribution

It provides the first detailed numerical evidence that self-helicity is conserved during quantum vortex reconnection, using high-resolution simulations and multiple computational methods.

Findings

Self-helicity remains conserved during quantum reconnection.

Vortex system length peaks at reconnection time.

Writhe and twist helicities are separately unchanged.

Abstract

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross- Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion and intrinsic twist of the reconnecting vortex rings.