Exact perturbative expansion of the transport coefficients of a normal low-temperature Fermi gas with contact interactions

• URL: http://arxiv.org/abs/2502.03423v2
• Date: Mon, 11 Aug 2025 20:26:12 GMT
• Title: Exact perturbative expansion of the transport coefficients of a normal low-temperature Fermi gas with contact interactions
• Authors: Pierre-Louis Taillat, Hadrien Kurkjian,
• Abstract summary: 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.<n>We extend the Landau-Salpeter equation to compute the collision amplitude beyond the forward-scattering limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $T_{\rm F}$ and much larger than the superfluid critical temperature $T_c$. Given recent advances in the precision of cold atom experiments, we provide exact results up to 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 wavenumber $k_{\rm F}$, follow $(1+\gamma k_{\rm F}a)/a^2$ up to corrections of order $O(a^0)$, with a positive coefficient $\gamma$ for the viscosity and negative one for the thermal conductivity and spin diffusivity. The inclusion of the correction linear in $k_{\rm F}a$ greatly improves the agreement with the recent measurement of the viscosity by the Yale group.

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