The ground state and vortices in a two-dimensional Bose gas confined in a harmonic trap

We study the ground state properties of a two-dimensional Bose gas in an harmonic trap potential using the recently proposed mean-field equation that takes into account the correct dimensionality effect. In contrast to the threedimensional case, the interaction term depends logarithmically on the scattering length and density. We compare our results with other approaches with various forms for the two-dimensional coupling. We also consider the vortex states and study the effects of density-dependent interactions on the formation of vortices.