Quantum Dynamics of a Bose Superfluid Vortex

Quantum vortex dynamics remain poorly understood despite decades of theoretical investigation. The vortex is a topological soliton, arising from the same medium as the quasiparticles with which it interacts. Hence 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 present a fully quantum-mechanical derivation of the vortex equation of motion valid at low temperatures where the normal fluid density is small. The resulting equation of motion is naturally expressed as a function of the dimensionless frequency $\tilde \Omega = \hbar \Omega/k_BT$. The usual Hall-Vinen/Iordanskii equations are valid when $\tilde \Omega \ll 1$ (the ``classical regime''), but elsewhere, the equations are strongly memory dependent. We will discuss the experimental implications of this frequency dependence in Bose superfluids and cold atomic gases.