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 $D_s\simeq 1.3\mathrm{\hslash }\mathrm{/}m$ approaching the quantum limit of diffusion for a particle of mass $m$. Conversely, the spin drag rate reaches a maximum value of ${\mathrm{\Gamma }}_{\text{sd}}\simeq 1.2k_B{T}_F\mathrm{/}\mathrm{\hslash }$ 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 $\sigma_s(\omega \to\infty) = \hbar^{1/2}C/3\pi(m\omega)^{3/2}$proportionaltotheTancontactdensity$C$. For the spin susceptibility ${\chi }_s(T)$ we find no downturn in the normal phase.