Semiclassical corrections to a static Bose-Einstein condensate at zero temperature

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensa te or, equivalently, by the hydrodynamic equations for the number density a nd current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical correcti ons to these equations for a general time-independent state of the condensa te, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be take n into account by adding a local correction term to the Gross-Pitaevskii eq uation. At second order in the Thomas-Fermi expansion, the semiclassical co rrections can be taken into account by adding local correction terms to the hydrodynamic equations. [S1050-2947(99)02609-8].