Abstract
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterize the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times. It follows that the Gausslinking number is a more appropriate definition of helicity for superfluids. Despite this, we explain how a quasiclassical limit can arise in a superfluid in which the continuum definition for helicity can be used. This provides a clear connection between a microscopic and a macroscopic description of a superfluid as provided by the Hall–Vinen–Bekarevich–Khalatnikov equations. This leads to consistency with the definition of helicity used for classical vortices.
Original language  English 

Article number  20160853 
Journal  Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 
Volume  473 
Issue number  2200 
DOIs  
Publication status  Published  5 Apr 2017 
Profiles

Hayder Salman
 School of Mathematics  Associate Professor in Applied Mathematics
 Centre for Photonics and Quantum Science  Member
 Quantum Fluids  Member
Person: Research Group Member, Academic, Teaching & Research