Spin-imbalanced homogeneous atomic fermi gas in two dimensions

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 $$g_{0}$$ 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 $$\mu ~$$ μ and U decrease as the box width increases. In addition, U increases linearly with $$g_{0}$$ g 0 in the repulsive interaction case and decreases as the magnitude of $$g_{0}$$ 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 $$\mu $$ μ 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.