Eighty years ago Eyring proposed that the shear viscosity of a liquid,
η, has a quantum limit
η≳nℏ where
n is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound
sη≥4πkBℏ for the ratio between the shear viscosity and the entropy density,
s. Using Dynamical Mean-Field Theory (DMFT) we calculate the shear viscosity and entropy density for a fermionic fluid described by a single band Hubbard model at half filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid
3He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid
1/T2 dependence, where
T is the temperature. With increasing temperature and interaction strength
U there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid
3He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge transfer salts.
We extract the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature $\ensuremath{\eta}/s$ is roughly equal to 1/2 in units of $\ensuremath{\hbar}/{k}_{B}$. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound $1/(4\ensuremath{\pi})$ than any other known liquid.
The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity to entropy density ( s ) for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as , is a measure of interaction strength in a quantum fluid where equality indicates a perfect quantum fluid. In this paper we study η / s in a Fermi gas in the unitary limit. We show that in addition to a local minimum for η / s at which obeys the lower bound, a more interesting result exists in the violation of the η / s lower bound due to the superfluid fluctuations above T c . To conclude, we examine the viscoelastic properties of the unitary Fermi gas. Previous work brought to light the connection between violation of the η / s bound and a viscoelastic response in the context of holographic solids. We ultimately find that, in addition to holographic solids, all Fermi liquids with a viscoelastic response produced by superfluid fluctuations can violate the universal η / s lower bound.
We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature
T limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature
Tc. A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.
In this paper we address the ratio of the shear viscosity to entropy density $\ensuremath{\eta}/s$ in bosonic and fermionic superfluids. A small $\ensuremath{\eta}/s$ is associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low-temperature transport associated with the quasiparticles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. Interestingly, we find that the transport properties of strict BCS and Bogoliubov superfluids have very similar structures, albeit with different quasiparticle dispersion relations. While there is a dramatic contrast between the power law and exponential temperature dependence for $\ensuremath{\eta}$ alone, the ratio $\ensuremath{\eta}/s$ for both systems is more similar. Specifically, we find the same linear dependence (on the ratio of temperature
T to inverse lifetime $\ensuremath{\gamma}(T))$ with $\ensuremath{\eta}/s\ensuremath{\propto}T/\ensuremath{\gamma}(T)$, corresponding to imperfect fluidity. By contrast, near the unitary limit of BCS-BEC superfluids a very different behavior results, which is more consistent with near-perfect fluidity.