Quantum Dynamics of a Bose Superfluid Vortex

We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid, in the temperature regime where the normal fluid density $ρ_n(T)$ is small. The coupling between the vortex "zero mode" and the quasiparticles has no term linear in the quasiparticle variables -- the lowest-order coupling is quadratic. We find that as a function of the dimensionless frequency $\tilde Ω= \hbar Ω/k_BT$, the standard Hall-Vinen/Iordanskii equations are valid when $\tilde Ω\ll 1$ (the "classical regime"), but elsewhere, the equations of motion become highly retarded, with significant experimental implications when $\tilde Ω\gtrsim 1$.