Fermi liquid behavior and Luttinger's theorem close to a diverging scattering length

Abstract

We derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first-order phase transition occurs in the normal phase as a function of the interaction strength. We also show that a volume change occurs at finite temperatures as we go through a divergence in the s-wave scattering length, in the normal phase. The first-order transition has a critical temperature, T *, above the BCS transition temperature. Also, we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.