Bose-Einstein condensation in variable dimensionality

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali-metal gases. The perturbation parameter is δ=1/κ, where κ depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the N⃗∞ Thomas-Fermi ground-state approximation of the Gross-Pitaevskii equation. The approximation presented here is well suited for calculating properties of states in three dimensions and in low-effective dimensionality, such as vortex states in a highly anisotropic trap.