  In this chapter, we describe three related studies of the universal physics
of two-component unitary Fermi gases with resonant short-ranged interactions.
First we discuss an ab initio auxiliary field quantum Monte Carlo technique for
calculating thermodynamic properties of the unitary gas from first principles.
We then describe in detail a Density Functional Theory (DFT) fit to these
thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and
its Asymmetric (ASLDA) generalization. We present several applications,
including vortex structure, trapped systems, and a supersolid
Larkin-Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent
extension to the density functional (TDDFT) which can describe quantum dynamics
in these systems, including non-adiabatic evolution, superfluid to normal
transitions and other modes not accessible in traditional frameworks such as a
Landau-Ginzburg, Gross-Pitaevskii, or quantum hydrodynamics.
