Shear Viscosity in the Strong Interaction Regime of a p-wave Superfluid Fermi Gas

Microscopic Approach to Shear Viscosities in Superfluid Gases: From BCS to BEC

We compute the shear viscosity, $η$, at general temperatures $T$, in a BCS-BEC crossover scheme which is demonstrably consistent with conservation laws. The study of $η$ is important because it constrains microscopic theories by revealing the excitation spectra. The onset of a normal state pairing gap and the contribution from pair degrees of freedom imply that $η$ at low $T$ becomes small, rather than exhibiting the upturn predicted by most others. Using the local density approximation, we find quite reasonable agreement with just-published experiments.

Boundary central charge from bulk odd viscosity - chiral superfluids

We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge $c$ of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of $c$. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are requ…

Shear Viscosity of Uniform Fermi Gases with Population Imbalance

The shear viscosity plays an important role in studies of transport phenomena in ultracold Fermi gases and serves as a diagnostic of various microscopic theories. Due to the complicated phase structures of population-imbalanced Fermi gases, past works mainly focus on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi gases with tunable attractive interactions at finite temperatures by using a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. In the unitary …

Medium effects and the shear viscosity of the dilute Fermi gas away from the conformal limit

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 $z=nλ^3/2$ is small. Here, $n$ is the density of the gas and $λ$ is the thermal wave length 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 …

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

We present a detailed analysis of the contribution of small-angle Nambu-Goldstone boson (phonon) collisions to the shear viscosity, $η$, in a superfluid atomic Fermi gas close to the unitarity limit. We show that the experimental values of the shear viscosity coefficient to entropy ratio, $η/s$, obtained at the lowest reached temperature can be reproduced assuming that phonons give the leading contribution to $η$. The phonon contribution is evaluated considering $1 \leftrightarrow 2$ processes and taking into account the finite size of the experimental system. In particular, for very low tempe…

Shear viscosity and damping of collective modes in a two-dimensional Fermi gas

We compute the shear viscosity of a two dimensional Fermi gas interacting via a short range potential with scattering length $a_{2d}$ in kinetic theory. We find that kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two dimensional gas is comparable to that of the three dimensional unitary gas. We use our results to compute the damping of collective modes in a trapped Fermi gas, and compare to experimental data recently obtained in E. Vogt et al., arXiv:1111.1173.

Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow

We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph et al. and measurements of the equation of state by Ku et al. We find that the shear viscosity to particle density ratio just above the critical temperature is $η/n|_{T_c}=0.41\pm 0.11$. We also obtain evidence that the shear viscosity to entropy density ratio has a …

The temperature evolution of the shear viscosity in a unitary Fermi gas

We present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with the bound for the shear viscosity originating from hydrodynamic fluctuations. Assuming smoothness of the frequency dependent shear viscosity eta(omega), we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper paring in the system. In order to preserve the hydrodynamic bound in QMC eta(omega) has…

Shear viscosity and spin diffusion in a two-dimensional Fermi gas

We investigate the temperature dependence of the shear viscosity and spin diffusion in a two-dimensional Fermi gas with contact interactions, as realized in ultra-cold 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, $η/s$, by a factor of three, and similarly for spin diffusion. The trap averaged viscosity agrees well with recent measurements by Vo…

Shear Viscosity of a Unitary Fermi Gas

We present the first ab initio determination of the shear viscosity eta of the Unitary Fermi Gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity to entropy density ratio eta/s. The minimum of eta/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being eta/s approx 0.2 hbar/kB, which almost saturates the Kovtun-Son-Starinets universal value hbar/(4 pi kB).

Shear viscosity and spin sum rules in strongly interacting Fermi gases

Fermi gases with short-range interactions are ubiquitous in ultracold atomic systems. In the absence of spin-flipping processes the number of atoms in each spin species is conserved separately, and we discuss the associated Ward identities. For contact interactions the spin conductivity spectral function sigma_s(omega) has universal power-law tails at high frequency. We derive the spin f-sum rule and show that it is not affected by these tails in d<4 dimensions. Likewise the shear viscosity spectral function eta(omega) has universal tails; in contrast they modify the viscosity sum rule in a ch…

相互作用二维费米液体中的剪切黏度

Shear viscosity in interacting two-dimensional Fermi liquids

针对中间温度下相互作用主导的二维电子气的流体动力学输运问题，提出数值精确的基展开法求解费米液体方程以计算剪切黏度，发现低温极限下存在非解析交换贡献，为费米液体响应研究提供了新平台。