Thomas-Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose-Einstein condensate

We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar-shaped, pancake-shaped, and spherical geometries. These also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our predictions, including analytic forms for the density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi and low-dimensional criteria.