Exact Relations for A Strongly-Correlated Fermi Gas With Large Scattering Length

A 2-component Fermi gas with a large and tunable scattering length $a$ is considered. If the interfermionic forces have a range much shorter than the average interparticle spacing, the characteristic de Broglie wavelength, and $\mid\! a\!\mid$, the system is in a universal regime in which the interaction is described by a single parameter, $a$. We show that the energy, the momentum distribution, the pressure, the change of energy during a real-time ramp of the scattering length, and the energy spectrum of such a Fermi gas satisfy a few simple \emph{exact} relations. The importance of the $C/k^4$ tails of the momentum distributions at large $k$ is stressed. Implications of these results for experiments on ultracold atomic Fermi gases near Feshbach resonances are discussed.