Superfluid phenomena can be explained in terms of the topologies of the order parameter and of the confining vessel. For example, currents in a toroidal vessel can be characterized by a discrete and conserved quantity, the winding number. In trapped Bose-Einstein condensates, the topology of the trap can be characterized by the topology of the Thomas-Fermi surface of its N-particle ground state. This can be altered during an experiment, so that a toroidal trap may deform into a more spherical shape, allowing an initially persistent current to decay into singly-quantized vortices. We investigate such a procedure numerically, and confirm that the Thomas-Fermi prescription for the trap topology gives an accurate picture of vortex formation.
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