Perfect fluids and bad metals: insights from ultracold Fermi gases

In this paper we address the ratio of the shear viscosity to entropy density η/s in bosonic and fermionic superfluids. A small η/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 quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the oneloop 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 quasi-particle dispersion relations. While there is a dramatic contrast between the power law and exponential temperature dependence for η alone, the ratio η/s for both systems is more similar. Specifically we find the same linear dependence (on the ratio of temperature T to inverse lifetime γ(T )) with η/s ∝ T /γ(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.

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“…This appears consistent with the observed differences between helium-3 and helium-4 superfluids [23].…”

Section: Discussionsupporting

confidence: 91%

Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

2014

Self Cite

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“…Near T c quantum statistics and pseudogap effects are likely to be important. These effects can be incorporated into kinetic theory, but a diagrammatic framework along the lines of [23][24][25] is likely to be more reliable.…”

Section: Discussionmentioning

confidence: 99%

“…Early studies of medium effects were reported in [21,22]. Medium effects are also included in the T -matrix approaches of Enss et al [23] and Levin et al [24,25].…”

Section: Introductionmentioning

confidence: 99%

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

Bluhm

Schäfer

2014

Phys. Rev. A

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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 as the quasi-particle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation (BEC) side of the resonance, in agreement with the result of recent experiments.

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“…For example, the viscosity of the classical ideal gas is exactly ε(T )τ p = nk B T τ p where n is particle density 17 . The kinetic approach to Fermi liquid theory similarly yields η F L ∼ ε(T )τ tr (T ) up to a constant close to unity 18,19 . In practice η F L turns out to be rather large because it scales with the large Fermi energy intrinsic to true metals.…”

Section: Introductionmentioning

confidence: 91%

Nearly perfect fluidity in a high-temperature superconductor

et al. 2014

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Perfect fluids are characterized as having the smallest ratio of shear viscosity to entropy density, η/s, consistent with quantum uncertainty and causality. So far, nearly perfect fluids have only been observed in the Quark-Gluon Plasma (QGP) and in unitary atomic Fermi gases (UFG), exotic systems that are amongst the hottest and coldest objects in the known universe, respectively. We use Angle Resolve Photoemission Spectroscopy (ARPES) to measure the temperature dependence of an electronic analogue of η/s in an optimally doped cuprate high temperature superconductor, finding it too is a nearly perfect fluid around, and above, its superconducting transition temperature T c .

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Perfect fluids and bad metals: insights from ultracold Fermi gases

Cited by 34 publications

References 75 publications

Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

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

Nearly perfect fluidity in a high-temperature superconductor

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