Low Temperature And High Temperature Expansion Of Thermodynamic Quantities In Unitary Fermi Gas

Since Bose-Einstein condensation of ideal Bose gas has been discovered experimentally, the ultra-cold Fermi gas has become a hotspot. The inter-particle interaction strength between different spin specie can be tuned by an external magnetic field. The so-called Feshbach resonance will be realized at certain magnetic field. At the same time, the scattering length between particles tends to infinity at this resonance point, while the cross section saturates the unitary limit. The Unitary Fermi gas is a strong interaction system. The only dominant length scale of the system at unitarity is the inter-particle spacing. The thermodynamics properties are universal because they are independent of any feature of atomic potentials. Compared to the balanced Fermi gas, the thermodynamics of unbalanced Fermi gas is more universal, which is the motivation of this paper.In the first part, the quasi-particle concept will be introduced for the strongly interacting quantum Fermi gas through the effective chemical potential containing the strong interaction and fluctuation information. The effective interaction energy of the polarized Fermi gas will be studied by the Dyson-Schwinger equation. The fluctuation effects will be investigated by the polarization tensor. The thermodynamic parametric equations are achieved by temperature Green’s function and the geometric mean susceptibility hypothesis. The low temperature expressions of energy, pressure and entropy can be achieved by using the Sommerfeld expansion to the parametric equations. The result at zero temperature obtained by geometric mean susceptibility hypothesis is consistent with that of Monte Carlo methods. The feature of phase transitions and thermodynamics at extremely low temperatures can be analyzed by drawing picture. The ratio between Landau parameters and bare particles can be got from heat capacity at constant pressure and heat capacity at constant volume.In the second part, we focus on the thermodynamic expression at high temperatures. The fugacity of system is infinitesimal in such a situation. Finally, we perform the virial expansions of energy and pressure. Furthermore, we obtain the second and third virial coefficients for the unbalanced unitary Fermi systems.