Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: Einternal = � 2 ΩC/4πam + ∑ ( � 2 k 2 /2m)(nkσ − C/k 4) where the external potential energy is not included, a is the scattering length, Ω is the volume, nkσ is the average number of fermions with wave vector k and spin σ, and C ≡ limk→ ∞ k 4 nk ↑ = limk→ ∞ k 4 nk↓. This result is a universal identity. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including the short-range structure of the one-body reduced density matrix and the pair correlation function, and the dimer-fermion scattering length, are also studied.

Перевод пока недоступен