Unitary Fermi Gas and the Challenge of Simple Q.M.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems we know, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UGF require Monte Carlo calculations. However, significant progress has been made with purely analytic methods. Notable, in 2005 Tan delivered a et of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high frequency power law decay of correlators as well as the right-hand-sides of shear and bulk viscosity sum rrules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibbrium.