Dilute Bose gas in a quasi-two-dimensional trap

We investigate the behaviour of a dilute quasi-two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature T. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation.