We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain nonhydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity that is solely a function of temperature, $\ensuremath{\eta}\ensuremath{\sim}{(mT)}^{3/2}$, as predicted by kinetic theory in the dilute limit.We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain nonhydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity that is solely a function of temperature, $\ensuremath{\eta}\ensuremath{\sim}{(mT)}^{3/2}$, as predicted by kinetic theory in the dilute limit.

arXiv:1505.00846Physical Review AOct 1, 201538 citations

Dissipation in finite Fermi systems

Sudhir R. Jain

arXiv:nucl-th/9912062Nuclear Physics AJun 1, 20007 citations

Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Free expansion and rotation

Thomas Schäfer

We investigate the expansion dynamics of a dilute Fermi gas at unitarity in the context of dissipative fluid dynamics. Our aim is to quantify the effects of shear viscosity on the time evolution of the system. We compare exact numerical solutions of the equations of viscous hydrodynamics to various approximations that have been proposed in the literature. Our main findings are (i) shear viscosity leads to characteristic features in the expansion dynamics; (ii) a quantitative description of these effects has to include reheating; (iii) dissipative effects are not sensitive to the equation of state $P(n,T)$ as long as the universal relation $P=\frac{2}{3}\mathcal{E}$ is satisfied; (iv) the expansion dynamics mainly constrains the cloud average of the shear viscosity.We investigate the expansion dynamics of a dilute Fermi gas at unitarity in the context of dissipative fluid dynamics. Our aim is to quantify the effects of shear viscosity on the time evolution of the system. We compare exact numerical solutions of the equations of viscous hydrodynamics to various approximations that have been proposed in the literature. Our main findings are (i) shear viscosity leads to characteristic features in the expansion dynamics; (ii) a quantitative description of these effects has to include reheating; (iii) dissipative effects are not sensitive to the equation of state $P(n,T)$ as long as the universal relation $P=\frac{2}{3}\mathcal{E}$ is satisfied; (iv) the expansion dynamics mainly constrains the cloud average of the shear viscosity.

arXiv:1008.3876Physical Review ADec 27, 201027 citations

The contact of the Fermi gas at unitarity

Scott Jensen, C. N. Gilbreth, Y. Alhassid

Bulletin of the American Physical SocietyMar 5, 20190 citations

Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity

Thomas Schäfer, Kevin Dusling

The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio $(P-\frac{2}{3}{\cal E})/P$ , where $P$ is the pressure and ${\cal E}$ is the energy density. In the high temperature limit this ratio scales as $\frac{zλ}{a}$ , where $z$ is the fugacity, $λ$ is the thermal wave length, and $a$ is the scattering length. We show that the bulk viscosity $ζ$ scales as the second power of this parameter, $ζ\sim (\frac{zλ}{a})^2 λ^{-3}$ .The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio $(P-\frac{2}{3}{\cal E})/P$, where $P$ is the pressure and ${\cal E}$ is the energy density. In the high temperature limit this ratio scales as $\frac{zλ}{a}$, where $z$ is the fugacity, $λ$ is the thermal wave length, and $a$ is the scattering length. We show that the bulk viscosity $ζ$ scales as the second power of this parameter, $ζ\sim (\frac{zλ}{a})^2 λ^{-3}$.

arXiv:1305.4688May 21, 20137 citations

P(n,T)

as long as the universal relation

P=\frac{2}{3}\mathcal{E}

is satisfied; (iv) the expansion dynamics mainly constrains the cloud average of the shear viscosity.

(P-\frac{2}{3}{\cal E})/P

, where

P

is the pressure and

{\cal E}

is the energy density. In the high temperature limit this ratio scales as

\frac{zλ}{a}

, where

z

is the fugacity,

λ

is the thermal wave length, and

a

is the scattering length. We show that the bulk viscosity

ζ

scales as the second power of this parameter,

ζ\sim (\frac{zλ}{a})^2 λ^{-3}