Quantum Dynamics of a Bose Superfluid Vortex

Abstract

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[subscript 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 [omega]~=[Latin small letter h with a stroke][omega]/k[subscript B]T, the standard Hall-Vinen-lordanskii equations are valid when [omega]~<<1 (the 'classical regime"0, but elsewhere, the equations of motion become highly retarded, with significant experimental implications when [omega]~[greater than or equivalent to]1.