Vortices in an Imperfect Bose Gas. IV. Translational Velocity

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 $\left(\frac{h}{4\pi \mathrm{mR}}\right)\ln \left(\frac{8R}{\alpha }\right)$, where $\alpha$ is a length the order of the core size. Both results agree with the predictions of classical hydrodynamics.