Vortices in an Imperfect Bose Gas. IV. Translational Velocity

Abstract

The translational velocity of a vortex with circulation $\frac{h}{m}$ in an imperfect Bose gas is calculated by considering the time dependence of the condensate wave function corresponding to a given initial configuration of vortices. Each vortex in a system of rectilinear vortices is shown to move with the local fluid velocity at its core; a vortex ring of radius $R$ is shown to move with velocity $(\frac{h}{4\ensuremath{\pi}\mathrm{mR}})\mathrm{ln}(\frac{8R}{\ensuremath{\alpha}})$, where $\ensuremath{\alpha}$ is a length the order of the core size. Both results agree with the predictions of classical hydrodynamics.