Abstract
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 straightforward
application of perturbation theory around the ideal Bose gas.
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