Vortex flux and Berry phase in a Bose-Einstein condensate confined in a toroidal trap

We study a system of large number of singly quantized vortices in a BEC confined in a rotating toroidal geometry. Analogous to the Meissner effect in supercomputers, we show that the external rotational field can be tuned to can cancel the Magnus field, resulting in a zero vortex flux. We also show that the Berry's phase for this system is directly related to the vortex flux.