Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1204.0270 · Physical Review Letters

Shear Viscosity of a Unitary Fermi Gas

Gabriel Wlazłowski, Piotr Magierski, Joaquín E. Drut

Published Jul 12, 2012• 44 citations
arXivHTMLPDF

Abstract

We present an ab initio determination of the shear viscosity $\ensuremath{\eta}$ 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 $\ensuremath{\eta}/s$. The minimum of $\ensuremath{\eta}/s$ appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being $(\ensuremath{\eta}/s{)}_{\mathrm{min}}\ensuremath{\approx}0.2\ensuremath{\hbar}/{k}_{B}$, which is close the Kovtun-Son-Starinets universal value $\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$.

DOI
10.1103/physrevlett.109.020406

Related papers

Temperature evolution of the shear viscosity in a unitary Fermi gas

Gabriel Wlazłowski, Piotr Magierski, Aurel Bulgac +1 more

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 $\ensuremath{\eta}(\ensuremath{\omega})$, we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. In order to preserve the hydrodynamic bound in QMC $\ensuremath{\eta}(\ensuremath{\omega})$ has to possess a sharp structure located in the vicinity of zero frequency which is not resolved by an analytic continuation procedure.

arXiv:1304.2283•Physical Review A•Jul 31, 2013•29 citations

Viscosity and scale invariance in the unitary Fermi gas

Tilman Enss, R. Haussmann, W. Zwerger

We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity $\eta(\omega)$ exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of $0.5 T_F$, thus invalidating a quasiparticle description. The ratio $\eta/s$ between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound $\hbar/(4\pi k_B)$ by a factor of about seven.

•Jan 20, 2016•164 citations

Perfect-fluid behavior of a dilute Fermi gas near unitary

Gabriel Wlazłowski, Wei Quan, Aurel Bulgac

We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength $\frac{1}{a{k}_{F}}$ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than ${10}^{9}$ atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.

arXiv:1504.02560•Physical Review A•Dec 21, 2015•19 citations

Determination of the Density and Temperature Dependence of the Shear Viscosity of a Unitary Fermi Gas Based on Hydrodynamic Flow

Marcus Bluhm, Jiaxun Hou, Thomas Schäfer

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, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.

arXiv:1704.03720•Physical Review Letters•Aug 10, 2017•36 citations

Shear viscosity of a superfluid Fermi gas in the unitarity limit

Gautam Rupak, Thomas Schäfer

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 ${T}_{c}$. 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 $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.

arXiv:0707.1520•Physical Review A•Nov 13, 2007•105 citations

Quantum critical transport in the unitary Fermi gas

Tilman Enss

The thermodynamic and transport properties of the unitary Fermi gas at finite temperature $T$ are governed by a quantum critical point at $T=0$ and zero density. We compute the universal shear viscosity to entropy ratio $\ensuremath{\eta}/s$ in the high-temperature quantum critical regime $T\ensuremath{\gg}|\ensuremath{\mu}|$ and find that this strongly coupled quantum fluid comes close to perfect fluidity $\ensuremath{\eta}/s=\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$. Using a controlled large-$N$ expansion, we show that already at the first nontrivial order the equation of state and the Tan contact density $C$ agree well with the most recent experimental measurements and theoretical Luttinger-Ward and bold diagrammatic Monte Carlo calculations.

arXiv:1204.1980•Physical Review A•Jul 12, 2012•46 citations
We present an ab initio determination of the shear viscosity \ensuremathη\ensuremath{\eta}\ensuremathη 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 \ensuremathη/s\ensuremath{\eta}/s\ensuremathη/s. The minimum of \ensuremathη/s\ensuremath{\eta}/s\ensuremathη/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being (\ensuremathη/s)min\ensuremath≈0.2\ensuremathℏ/kB(\ensuremath{\eta}/s{)}_{\mathrm{min}}\ensuremath{\approx}0.2\ensuremath{\hbar}/{k}_{B}(\ensuremathη/s)min​\ensuremath≈0.2\ensuremathℏ/kB​, which is close the Kovtun-Son-Starinets universal value \ensuremathℏ/(4\ensuremathπkB)\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})\ensuremathℏ/(4\ensuremathπkB​).
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 $\ensuremath{\eta}(\ensuremath{\omega})$, we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. In order to preserve the hydrodynamic bound in QMC $\ensuremath{\eta}(\ensuremath{\omega})$ has to possess a sharp structure located in the vicinity of zero frequency which is not resolved by an analytic continuation procedure.
We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity η(ω)\eta(\omega)η(ω) exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of 0.5TF0.5 T_F0.5TF​, thus invalidating a quasiparticle description. The ratio η/s\eta/sη/s between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound ℏ/(4πkB)\hbar/(4\pi k_B)ℏ/(4πkB​) by a factor of about seven.
We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength 1akF\frac{1}{a{k}_{F}}akF​1​ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than 109{10}^{9}109 atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.
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, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.
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 TTT 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{T}_{c}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 $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.
The thermodynamic and transport properties of the unitary Fermi gas at finite temperature TTT are governed by a quantum critical point at T=0T=0T=0 and zero density. We compute the universal shear viscosity to entropy ratio $\ensuremath{\eta}/s$ in the high-temperature quantum critical regime $T\ensuremath{\gg}|\ensuremath{\mu}|$ and find that this strongly coupled quantum fluid comes close to perfect fluidity $\ensuremath{\eta}/s=\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$. Using a controlled large-NNN expansion, we show that already at the first nontrivial order the equation of state and the Tan contact density CCC agree well with the most recent experimental measurements and theoretical Luttinger-Ward and bold diagrammatic Monte Carlo calculations.