Quantum mechanical limitations to spin diffusion in the unitary Fermi gas

TL;DR

This paper investigates the fundamental quantum limits of spin diffusion in the unitary Fermi gas, revealing minimal diffusivity and maximal spin drag rate, and analyzes the frequency-dependent spin conductivity and susceptibility.

Contribution

It provides the first detailed calculation of spin transport properties in the strongly interacting regime using Luttinger-Ward theory, highlighting quantum limits and universal behaviors.

Findings

Spin diffusivity reaches a minimum of about 1.3 ħ/m.

Spin drag rate peaks at approximately 1.2 k_B T_F/ħ.

Spin conductivity exhibits a broad Drude peak with a universal high-frequency tail.

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