Quantum Corrections to a Static Bose-Einstein Condensate at Zero Temperature

A previous calculation of the leading corrections from quantum field fluctuations to the ground state of a trapped Bose-Einstein condensate at zero temperature is extended to general time-independent states, including vortex states. The calculation is streamlined by using dimensional regularization to regularize both ultraviolet and infrared divergences. We calculate the leading quantum corrections to the mean-field equations for the condensate through first order in the semiclassical expansion in powers of √ ρa3, where ρ is the local density and a is the scattering length. The Thomas-Fermi expansion is used to express the matrix elements in this equation in terms of local quantities. In the Thomas-Fermi limit, the corrections can be taken into account by adding a local term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the corrections can be taken into account by adding local terms to the hydrodynamic equations for the number density and the current density.