Ground-state properties and collective excitations in a 2D Bose-Einstein condensate with gravity-like interatomic attraction

We study the ground-state properties of a Bose-Einstein condensate (BEC) with the short-range repulsion and gravitylike 1/r interatomic attraction in two-dimensions (2D). Using the variational approach, we obtain the ground-state energy and show that the condensate is stable for all interaction strenghts in 2D. We also determine the collective excitations at zero temperature using the time-dependent variational method. We analyze the properties of the Thomas-Fermi-gravity (TF-G) and gravity (G) regimes.