A study of trapped Bose gas beyond mean-field theory
  We study the ground-state properties of dilute Bose gas confined to both isotropic and anisotropic traps to assess the accuracy of Gross-Pitaevskii (GP) theory. To go beyond GP approximation we use Huang-Yang theory of interatomic interaction energy for hard-sphere Bose gas and use a variational method to solve the resulting modified GP equation. We also make an analytic estimate of the corrections due to higher-order terms in the interatomic interaction energy. We find that the corrections are of the order of 1 percent. However, there is a qualitative change in the density profile due to presence of logarithimic term in the interaction energy for large N (number of atoms) 
Arup Banerjee and Manoranjan P. Singh