Helicity in Superfluids: conservation and the classical limit

Hridesh Kedia, Dustin Kleckner, Davide Proment +1 more

Hridesh Kedia, Dustin Kleckner, Davide Proment +1 more

Xiaohui Li, Ting-Pong Choy, Tai Kai Ng

Hayder Salman

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 Gauss-linking number is a more appropriate definition of helicity for superfluids. Despite this, we explain how a quasi-classical 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.

Carlo F. Barenghi, Luca Galantucci, Nicholas G. Parker +1 more

Helicity - a quadratic invariant of the classical Euler equation like the energy - plays a fundamental role in turbulent flows, controlling the strength of the nonlinear interactions which cascade energy to smaller length scales. The growing interest in turbulent superfluid liquid helium, a disordered state of quantum matter consisting of a tangle of vortex lines - triggers a natural question: what is superfluid helicity ? The most used model of superfluid vortex lines is based on the Gross-Pitaevskii equation for a weakly interacting Bose gas. In this mean field model, unfortunately, helicity is ill-defined, as vorticity and velocity are singular on the centerline of the vortex. Here we show that by taking into account more realistic features of the vortex core arising from N-body quantum mechanics simulations, which account for the stronger atom interactions occurring in a liquid, the classical definition of helicity can be extended to superfluid helium. We also present results of numerical experiments which reveal the role and physical meaning of helicity in superfluid turbulence.