Exact Perturbative Expansion of the Transport Coefficients of a Normal Low-Temperature Fermi Gas with Contact Interactions

We compute the shear viscosity, thermal conductivity, and spin diffusivity of a Fermi gas with short-range interactions in the Fermi liquid regime of the normal phase, that is, at temperatures T much lower than the Fermi temperature TF and larger than the superfluid critical temperature Tc. In line with recent advances in the precision of cold atom experiments, we provide exact results up to the second order in the interaction strength. We extend the Landau-Salpeter equation to compute the collision amplitude beyond the forward-scattering limit, covering all collisions on the Fermi surface. We treat the collision kernel exactly, leading to significant corrections beyond relaxation-time or variational approximations. The transport coefficients, as functions of the s wave scattering length a and Fermi wave number kF, follow (1+γkFa)/a² up to corrections of order O(a⁰), with a positive coefficient γ for the viscosity and negative one for the thermal conductivity and spin diffusivity.