Quantum Vortex Dynamics: Results for a 2-d Superfluid

We model vortex dynamics in a 2-dimensional Bose superfluid using the Thompson-Stamp (TS) equations of motion, which describes both the classical Hall-Vinen-Iordanskii (HVI) dynamical regime and the fully developed quantum regime, and the crossover between them. The TS equations can be written in the form of a quantum Langevin equation. Analytic solutions are given for all of these regimes for a single vortex in a 2-dimensional system. In the classical regime we include the vortex inertial and Langevin noise terms, which are dropped in the usual HVI analysis. In the quantum and crossover regimes the effect of memory terms is important, and leads to clear differences from the classical predictions.