Velocity of vortices in inhomogeneous Bose-Einstein condensates

Details Velocity of vortices in inhomogeneous Bose-Einstein condensates Velocity of vortices in inhomogeneous Bose-Einstein condensates

2005-08-08

arxiv.org/abs/cond-mat/0508195v3

Proc. Natl. Acad. Sci. 103, 7978 (2006)

Physics

Condensed Matter

Other Condensed Matter

5 pages, one .eps figure. Published version

Scientific paper

10.1073/pnas.0602541103

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity. We indicate how Kelvin's conservation of circulation theorem is compatible with the velocity of the vortex center being different from the local fluid velocity. Finally we derive an exact wave function for a single vortex near the rotation axis in a weakly interacting system, from which we derive the vortex precession rate.

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