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.

Keywords:

• degenerate Fermi gas
• Fermi liquid
• Feshbach resonance
• superfluidity

Notes

Notes

1. The free gas Fermi Surface (FS) volume is preserved when the interaction is turned on, see 3.

2. The momentum of the collective modes corresponding to this critical temperatures is of order . Thus, .