Tunnelling of topological line defects in strongly coupled superfluids

The geometric theory of vortex tunnelling in superfluid liquids is develope d. Geometry rules the tunnelling process in the approximation of an incompr essible superfluid, which yields the identity of phase and configuration sp ace in the vortex collective co-ordinate. To exemplify the implications of this approach to tunnelling, we solve explicitly for the two-dimensional mo tion of a point vortex in the presence of an ellipse, showing that the hydr odynamic collective co-ordinate description limits the constant energy path s allowed for the vortex in configuration space. We outline the experimenta l procedure used in helium II to observe tunnelling events, and compare the conclusions we draw to the experimental results obtained so far. Tunnellin g in Fermi superfluids is discussed, where it is assumed that the low energ y quasiparticle excitations localised in the vortex core govern the vortex dynamical equations. The tunnelling process can be dominated by Hall or dis sipative terms, respectively be under the influence of both, with a possibl e realization of this last intermediate case in unconventional, high-temper ature superconductors.