Variational approach to the dilute Bose gas

We study the weakly interacting Bose gas in both two and three dimensions using a variational approach. In particular we construct the thermodynamic potential of the gas to within ladder approximation and find by minimization an accurate mean-field description of the dilute Bose gas. Using spin-polarized atomic hydrogen as a specific example. we obtain an improved description of the Bose-Einstein condensed phase in three dimensions, and a signature of a phase transition in two dimensions. The latter cannot be found by a straightforward application of perturbation theory around the ideal Bose gas.