Transport in Fermi Hubbard models: lessons from weak coupling

In the absence of phase transitions, all of the strong coupling phenomena in cold atom experiments are continuously connected to physics at weak coupling. I will report on quantum Boltzman equation calculations of resistivity in the Fermi Hubbard model. Here the only mechanism for momentum relaxation is Umklapp scattering -- where quantum coherent two-particle scattering deposits momentum into a perfect lattice. At temperatures large compared to the bandwidth the scattering rates are temperature independent but resistivity nonetheless grows linearly with temperature because of band-filling effects. At temperature small compared to the bandwidth the resistivity generically has the Fermi-liquid form, $\rho\propto T^2$. The temperature of the crossover from quadratic to linear behavior depends on the filling, vanishing at half-filling -- where the resistivity is approximately linear for all temperatures. I will also report on a simple, yet quantitatively accurate, Gutzwiller Ansatz based calculation of the compressibility.