Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases

Understand

We show that the universal $1/k^4$ tail in the momentum distribution of dilute Fermi gases implies that the spectral function $A(\kk,\omega)$ must have weight below the chemical potential for large momentum $k \gg k_F$, with observable consequences in RF spectroscopy experiments.

• We find that this incoherent spectral weight is centered about $\omega \simeq - \epsilon(\kk)$ in a range of energies of order $v_F k$.
• This "bending back" in the dispersion, while natural for superfluids, is quite surprising for normal gases.
• This universal structure is present in the hard-sphere gas as well as the Fermi liquid ground state of the highly imbalanced, attractive gas near unitarity.