The effect of interactions on Bose-Einstein condensation in a two-dimensional harmonic trap

A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed phase as the temperature is lowered. Its density profile and energy are identical to that of an ideal gas obeying the fractional exclusion statistics of Haldane. PACS: ~03.75.Fi, 05.30.Jp, 67.40.Db, 05.30.-d