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arXiv:1108.5487 · AIP conference proceedings

Nearly perfect fluidity in the dilute Fermi gas: An update

Thomas Schäfer

Published Jan 1, 2012• 0 citations
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Abstract

In this contribution we summarize recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and present new results on the structure of second order terms in the gradient expansion. We also discuss predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We summarize current constraints on the shear viscosity to entropy density ratio η/s.

DOI
10.1063/1.3700673

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In this contribution we summarize recent results on the transport properties of strongly correlated dilute Fermi gases. We discuss the hydrodynamic equations in the normal phase and present new results on the structure of second order terms in the gradient expansion. We also discuss predictions from kinetic theory, and show how these predictions can be tested using experimental data on elliptic flow. We summarize current constraints on the shear viscosity to entropy density ratio η/s.
Abstract. In this contribution we summarize recent progress in understanding the shear viscosity of strongly correlated dilute Fermi gases. We discuss predictions from kinetic theory, and show how these predictions can be tested using recent experimental data on elliptic flow. We find agreement between theory and experiments in the high temperature regime T TF, where TF is the the temperature where quantum degeneracy effects become important. In the low temperature regime, T ∼ TF, the strongest constraints on the shear viscosity come from experimental studies of the damping of collective modes. These experiments indicate that η/s ∼< 0.5h̄/kB, where η is the shear viscosity and s is the entropy density.
In this contribution we summarize recent progress in understanding the shear viscosity of strongly correlated dilute Fermi gases. We discuss predictions from kinetic theory, and show how these predictions can be tested using recent experimental data on elliptic flow. We find agreement between theory and experiments in the high temperature regime T≫TFT\gg T_FT≫TF​, where TFT_FTF​ is the the temperature where quantum degeneracy effects become important. In the low temperature regime, T∼TFT\sim T_FT∼TF​, the strongest constraints on the shear viscosity come from experimental studies of the damping of collective modes. These experiments indicate that $η/s\lsim 0.5\hbar/k_B$, where ηηη is the shear viscosity and sss is the entropy density.
Using the $\ensuremath{\varepsilon}$-expansion technique, we compute $\ensuremath{\eta}/s$, where $\ensuremath{\eta}$ is the shear viscosity and sss is the entropy density of the normal phase of unitary Fermi gas in $d=4\ensuremath{-}\ensuremath{\varepsilon}$ dimensions to leading order (LO) in $\ensuremath{\varepsilon}$. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\ensuremath{\varepsilon}}^{2}$, which is LO. The LO result is temperature independent with $\ensuremath{\eta}/s\ensuremath{\simeq}(0.11/{\ensuremath{\varepsilon}}^{2})(\ensuremath{\hbar}/{k}_{B})$. The d=3d=3d=3 prediction for $\ensuremath{\eta}/s$ exceeds the $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{B}$ bound by a factor of about 1.41.41.4.
This thesis considers out-of-equilibrium dynamics of strongly interacting non-relativistic Fermi gases in several two and three dimensional geometries. The tools of second-order hydrodynamics and gauge-gravity duality will be utilized to address this system. Many of the themes of this work are motivated by the observed similarities in transport properties between strongly interacting Fermi gases and other very different strongly interacting quantum fluids such as the quark-gluon plasma, high temperature superconductors, and quantum field theories described by gauge-gravity duality. In particular, these systems all nearly saturate the conjectured lower bound on the ratio of shear viscosity to entropy density η/s≥ℏ/(4πkB)η/s \geq \hbar/(4 πk_B)η/s≥ℏ/(4πkB​) coming from the AdS/CFT correspondence. Among other things, this observation, in conjunction with current experiment and data analysis in atomic, condensed matter, and nuclear physics lends itself to the following questions: How perfect of a fluid is the strongly interacting Fermi gas, and can one find a more stringent constraint on η/sη/sη/s in Fermi gases? Do the similarities in transport properties among strongly interacting quantum systems extend beyond dynamics controlled by the hydrodynamical shear viscosity? In regards to the first question, by utilizing second-order hydrodynamics, it will be demonstrated that higher-order collective modes of a harmonically trapped Fermi gas may serve as a more sensitive probe of the shear viscosity. For the second question, both second-order hydrodynamics and a gravity dual theory are used to make predictions about dynamics occurring on short timescales where hydrodynamics is expected to break down. In particular the appearance of a class of "non-hydrodynamic" collective modes not contained within a Navier-Stokes description of the strongly interacting Fermi gas will be discussed.
We review the modern view of fluid dynamics as an effective low-energy, long-wavelength theory of many-body systems at finite temperature. We introduce the concept of a nearly perfect fluid, defined by a ratio η/s of shear viscosity to entropy density of order ℏ/kBor less. Nearly perfect fluids exhibit hydrodynamic behavior at all distances down to the microscopic length scale of the fluid. We summarize arguments that suggest that there is fundamental limit to fluidity, and we review the current experimental situation of measurements of η/s in strongly coupled quantum fluids.