The challenge of moving topological defects in quantum matter

I have really enjoyed this week at the Australasian Workshop on Emergent Quantum Matter. My UQ colleague Matt Davis is to be congratulated for putting together an excellent program. There was nice balance of cold atom and solid state talks.

Is there anything that stood out to me?
Yes. Vortices, (Josephson) phase coherence, and dimensional crossovers. Vortices kept coming up and remain a fascinating and perplexing problem.
Vortices are mesoscopic, intermediate between the microscopic (atomic) and macroscopic scales. The length scale associated with them is emergent. They have some quantum properties (quantised circulation) but obey classical equations of motion, but interact with microscopic degrees of freedom (quasi-particles and phonons).

When one has a broken symmetry vortices are novel emergent low energy excitations. They are topological defects in the order parameter. Given how much they have been studied in superfluid 4He and superconductors one would think they were pretty well understood. However, this is not the case. What is particularly poorly understood is the dynamics of these objects.

Stephen Eckel described some beautiful experiments at NIST that recently investigated  Josephson type junctions in atomic BECs. My immediate question was how was this any different from landmark experiments performed by Davis and Packard in superfluid 3He?  In those experiments the superfluid "healing" (or coherence) length is quite small and there is not a single weak link but many apertures. The origin of the coupling between these links is not clear.
It was also interesting that a key consulting role in these experiments was played by Chris Lobb, an expert on solid state Josephson junctions.

Victor Galitski and Joachim Brand both described theory motivated by recent fermionic cold atom experiments which measured a large mass (both inertial and gravitational, the two are different) for solitons in a quasi-one-dimensional superfluid. Victor discussed recent theoretical calculations based on exact solution of the dynamical Bogoliubov-de Gennes (BdG) equations.

The question of how vortices and quasi-particles interact and the dynamics of a single vortex in a Bose superfluid is highly controversial. Theoretical calculations of the mass of a vortex range from zero to infinity! A brief introduction, including key references, is in this PRL.

Dimensionality matters. Solitons and Luttinger liquid only exist in strictly one dimension. The Berezinskii-Kosterlitz-Thouless transition strictly only exists in two dimensions. However, what happens in quasi-one or quasi-two-dimensional systems is not completely clear, inspite of a lot of theoretical work. Some ultra cold atom experiments may be able to address these questions of dimensional crossover.