Variational HFB Equations in the Thomas-Fermi Limit for Ultracold Trapped Gases

We derive variationally the HFB equations for a trapped self-interacting Bose gas at finite temperature. In the Thomas-Fermi limit, we obtain simple expressions for the condensate, the non condensate and the anomalous densities. Their behavior in terms of the condensate fraction meets qualitatively the experimental data. In particular, the non condensate and the anomalous densities are peaked at the center of the trap and not at the edges as predicted by the self-consistent HFB calculations.