k^-3 superfluid spectrum of highly curved interacting quantum vortices

TL;DR

This paper predicts a k^-3 superfluid spectrum for highly curved quantum vortices using differential geometry, aligning with simulation results of turbulent superfluidity.

Contribution

It introduces a geometric approach to derive the superfluid spectrum of interacting quantum vortices with arbitrary curvature and torsion.

Findings

Spectrum scales as k^-3 for highly curved vortices

Predicted spectrum matches quantum turbulence simulations

Supports geometric modeling of vortex interactions

Abstract

Presented is a prediction, based on the Frenet-Serret differential geometry of space curves, that the wave number dependence of the average kinetic energy per unit length of two mutually interacting highly curved quantum vortex scales as k^-3. The interacting quantum vortices are helical in shape, supporting circularly polarized counter-propagating waves, with arbitrary curvature and torsion. This power-law spectrum agrees with the high-k spectrum found in precise quantum simulations of turbulent superfluidity with tangle of highly curved and excited quantum vortices.