Vortices in an Imperfect Bose Gas. IV. Translational Velocity

The translational velocity of a vortex with circulation 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 (h4πmR)ln(8Rα), where α is a length the order of the core size. Both results agree with the predictions of classical hydrodynamics.