Tunnelling of topological line defects in strongly coupled superfluids

TL;DR

This paper develops a geometric theory of vortex tunnelling in superfluid liquids, analyzing the process through collective coordinates, and compares theoretical predictions with experimental observations in helium II and Fermi superfluids.

Contribution

It introduces a geometric framework for vortex tunnelling in superfluids and explicitly solves vortex motion in two dimensions, linking theory with experimental data.

Findings

Hydrodynamic collective coordinates limit vortex paths in configuration space.

Explicit solution for vortex motion in an elliptical boundary.

Comparison of tunnelling theory with helium II experiments.

Abstract

The geometric theory of vortex tunnelling in superfluid liquids is developed. Geometry rules the tunnelling process in the approximation of an incompressible superfluid, which yields the identity of phase and configuration space in the vortex collective co-ordinate. To exemplify the implications of this approach to tunnelling, we solve explicitly for the two-dimensional motion of a point vortex in the presence of an ellipse, showing that the hydrodynamic collective co-ordinate description limits the constant energy paths allowed for the vortex in configuration space. We outline the experimental procedure used in helium II to observe tunnelling events, and compare the conclusions we draw to the experimental results obtained so far. Tunnelling in Fermi superfluids is discussed, where it is assumed that the low energy quasiparticle excitations localised in the vortex core govern the vortex dynamical equations. The tunnelling process can be dominated by Hall or dissipative terms, respectively be under the influence of both, with a possible realization of this last intermediate case in unconventional, high-temperature superconductors.