TOD

Abstract

I will present a method for numerically building a quantum vortex knot state in the single scalar field wave function of a Bose-Einstein condensate. I will show how the two topologically simplest vortex knots wrapped over a torus evolve and may preserve their shapes by reporting results of the integration in time of the governing Gross-Pitaevskii equation.

In particular, I will focus on how the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: in a first approximation it is linear and, for smaller ratio, the knot travels faster. Finally, I will display mechanisms of vortex breaking by reconnections which produce simpler vortex rings whose number depends on initial knot topology.