Helicity conservation and twisted Seifert surfaces for superfluid vortices

Area of Science:

• Fluid dynamics
• Condensed matter physics
• Quantum hydrodynamics

Background:

• Helicity is a key invariant for classical vortices.
• Superfluid vortices exhibit complex dynamics requiring specialized theoretical frameworks.
• Understanding superfluid vortex properties is crucial for fields like quantum turbulence and Bose-Einstein condensates.

Purpose of the Study:

• To derive the contributions to helicity for superfluid vortices from first principles.
• To investigate the applicability of the continuum definition of helicity to superfluids.
• To establish a connection between microscopic and macroscopic descriptions of superfluid vortices.

Main Methods:

• Derivation of helicity contributions for superfluid vortices starting from the continuum definition.
• Analysis of the Seifert framing and its implications for superfluid helicity.
• Investigation of the quasi-classical limit for superfluid helicity.

Main Results:

• An internal twist contribution to helicity emerges naturally from the derivation.
• The continuum definition of helicity for superfluids is found to be trivially zero.
• The Gauss-linking number is identified as a more suitable helicity definition for superfluids.
• A quasi-classical limit is identified where the continuum helicity definition becomes applicable.

Conclusions:

• The study provides a rigorous derivation of helicity contributions in superfluid vortices.
• The Gauss-linking number is proposed as the appropriate measure of helicity for superfluids.
• The findings bridge microscopic and macroscopic descriptions of superfluids, aligning with classical vortex theory in a specific limit.