  Using the finite-temperature path integral Monte Carlo method, we investigate
dilute, trapped Bose gases in a quasi-two dimensional geometry. The quantum
particles have short-range, s-wave interactions described by a hard-sphere
potential whose core radius equals its corresponding scattering length. The
effect of both the temperature and the interparticle interaction on the
equilibrium properties such as the total energy, the density profile, and the
superfluid fraction is discussed. We compare our accurate results with both the
semi-classical approximation and the exact results of an ideal Bose gas. Our
results show that for repulsive interactions, (i) the minimum value of the
aspect ratio, where the system starts to behave quasi-two dimensionally,
increases as the two-body interaction strength increases, (ii) the superfluid
fraction for a quasi-2D Bose gas is distinctly different from that for both a
quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a
quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true
3D system with increasing temperature, and shows a stronger dependence on the
interaction strength, (iii) the superfluid fraction for a quasi-2D Bose gas
lies well below the values calculated from the semi-classical approximation,
and (iv) the Kosterlitz-Thouless transition temperature decreases as the
strength of the interaction increases.
