Quantum mechanical limitations to spin diffusion in the unitary Fermi gas

Abstract

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

5 pages, 4 figures; published version

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