Abstract
Two-dimensional spin-imbalanced homogeneous gas trapped in a hard box is studied within the static fluctuation approximation (SFA). The effects of temperature, tarp size, interaction strength g(0) and polarization on the thermodynamic properties are investigated. In the quantum regime, the energy U is found to be a parabolic function of T. The heat capacity and entropy increase with the width of the box indicating that these quantities are non-intensive quantities for finite size system, whereas the chemical potential mu and U decrease as the box width increases. In addition, U increases linearly with g(0) in the repulsive interaction case and decreases as the magnitude of g(0) of attractive potential increases. The results are compared to those obtained within the Diffusion Monte Carlo method with Fixed Node approximation, the self-consistent fluctuation theory, the virial expansion, and other experimental results. Our results for mu are compared to the theoretical results obtained by the virial-expansion method for a gas in free space, as well as to the experimental results for a gas in a harmonic trap. We have found that the results depend on the type of trap.