  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.
