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arXiv:2211.06314 · Physical Review A

Transport in p -wave-interacting Fermi gases

Jeff Maki, Tilman Enss

Published Feb 22, 2023• 7 citations
arXivHTMLPDF

Abstract

The scattering properties of spin-polarized Fermi gases are dominated by $p$-wave interactions. Besides their inherent angular dependence, these interactions differ from their $s$-wave counterparts as they also require the presence of a finite effective range in order to understand the low-energy properties of the system. In this article we examine how the shear viscosity and thermal conductivity of a three-dimensional spin-polarized Fermi gas in the normal phase depend on the effective range and the scattering volume in both the weakly and the strongly interacting limits. We show that, although the shear viscosity and the thermal conductivity both explicitly depend on the effective range near resonance, the Prandtl number which parametrizes the ratio of momentum to thermal diffusivity does not have an explicit interaction dependence both at resonance and for weak interactions in the low-energy limit. In contrast to $s$-wave systems, $p$-wave scattering exhibits an additional resonance at weak attraction from a quasi-bound state at positive energies, which leads to a pronounced dip in the shear viscosity at specific temperatures.

DOI
10.1103/physreva.107.023317

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The scattering properties of spin-polarized Fermi gases are dominated by ppp-wave interactions. Besides their inherent angular dependence, these interactions differ from their sss-wave counterparts as they also require the presence of a finite effective range in order to understand the low-energy properties of the system. In this article we examine how the shear viscosity and thermal conductivity of a three-dimensional spin-polarized Fermi gas in the normal phase depend on the effective range and the scattering volume in both the weakly and the strongly interacting limits. We show that, although the shear viscosity and the thermal conductivity both explicitly depend on the effective range near resonance, the Prandtl number which parametrizes the ratio of momentum to thermal diffusivity does not have an explicit interaction dependence both at resonance and for weak interactions in the low-energy limit. In contrast to sss-wave systems, ppp-wave scattering exhibits an additional resonance at weak attraction from a quasi-bound state at positive energies, which leads to a pronounced dip in the shear viscosity at specific temperatures.
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_{F} and larger than the superfluid critical temperature T_{c}. In line with recent advances in the precision of cold atom experiments, we provide exact results up to the 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 wave number k_{F}, follow (1+γk_{F}a)/a^{2} up to corrections of order O(a^{0}), with a positive coefficient γ for the viscosity and negative one for the thermal conductivity and spin diffusivity.
The transport properties of one-dimensional Fermi gases at low temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipative effects, one needs to examine interactions beyond the LL model. In this work, we provide a simple model that allows for a direct microscopic calculation of the bulk viscosity, namely, the one-dimensional spin polarized ppp-wave Fermi gas. To leading order in the finite interaction strength, we find that the bulk viscosity is finite and consistent with the requirement of scale symmetry. We further show that the bulk viscosity satisfies the Bose-Fermi duality relating the weakly interacting limit of the spin polarized Fermi gas to the strongly interacting limit of the Lieb-Liniger model and vice versa. This work establishes the bulk viscosity to leading order in scale-breaking interactions in both the strongly and weakly interacting limits for both high and low temperatures.
We investigate the temperature dependence of the shear viscosity and spin diffusion in a two-dimensional Fermi gas with contact interactions, as realized in ultracold atomic gases. We describe the transport coefficients in terms of a Boltzmann equation and present a full numerical solution for the degenerate gas. In contrast to previous works we take the medium effects due to finite density fully into account. This effect reduces the viscosity-to-entropy ratio $\ensuremath{\eta}/s$ by a factor of 3, and similarly for spin diffusion. The trap-averaged viscosity agrees well with recent measurements by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].
We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=n{\ensuremath{\lambda}}^{3}/2$ is small. Here, nnn is the density of the gas and $\ensuremath{\lambda}$ is the thermal wavelength of the fermions. At leading order in the fugacity expansion, the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order, medium effects modify the scattering amplitude as well as the quasiparticle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation side of the resonance, in agreement with the result of recent experiments.
We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters, which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit ∼ℏ/ m in the unitarity regime, where m is the particle mass. Finally, we derive a value for the low-temperature shear viscosity in the normal phase from the Landau parameters.