Quantum Mechanical Limitations to Spin Diffusion in the Unitary Fermi Gas

We compute spin transport in the unitary Fermi gas using the strong-coupling Luttinger-Ward theory. In the quantum degenerate regime the spin diffusivity attains a minimum value of D-s similar or equal to 1.3 (h) over bar /m approaching the quantum limit of diffusion for a particle of mass m. Conversely, the spin drag rate reaches a maximum value of Gamma(sd) similar or equal to 1.2k(B)T(F)/(h) over bar in terms of the Fermi temperature T-F. The frequency-dependent spin conductivity sigma(s)(omega) exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail sigma(s)(omega --> infinity) = (h) over bar C-1/2/3 pi(m omega)(3/2) proportional to the Tan contact density C. For the spin susceptibility chi(s)(T) we find no downturn in the normal phase.