Virial theorems for vortex states in a confined Bose-Einstein condensate

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.