Vortex precession and exchange in a Bose-Einstein condensate

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using method constrained optimization. In non-rotating axially symmetric trap, core single vortex precesses around trap center and, at same time, phase its wave function shifts constant rate. The precession velocity, speed shift, and distance between center, depend continuously on value conserved angular momentum that is carried by entire condensate. case pair identical vortices, engages an emergent gauge field their relative coordinate, with flux equal to ratio shift velocities.