Bose-Einstein condensation in trapped bosons: A Variational Monte Carlo   analysis
  Several properties of trapped hard sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single particle Gaussian and a hard sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and non-condensate properties to the hard sphere radius and the number of particles. Special attention is given to diagonalizing the one body density matrix and obtaining the corresponding single particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital with highest occupation. The effect of interaction on other quantities such as the ground state energy, the mean radial displacement, and the momentum distribution are calculated as well. Results are compared with Mean Field theory in the dilute limit. 
J. L. DuBois, H. R. Glyde