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:cond-mat/0701251 · Physical Review A

Ratio of shear viscosity to entropy density for trapped fermions in the unitarity limit

Thomas Schäfer

Published Dec 20, 2007• 106 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.76.063618

Related papers

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

Shear viscosity of strongly interacting fermionic quantum fluids

Nandan Pakhira, Ross H. McKenzie

Eighty years ago Eyring proposed that the shear viscosity of a liquid, $η$, has a quantum limit $η\gtrsim n\hbar$ 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 $\fracη{s}\geq \frac{\hbar}{4πk_{B}}$ 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 $^{3}$He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid $1/T^{2}$ 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 $^{3}$He. 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.

arXiv:1504.07131•Physical Review B•Sep 1, 2015•9 citations

Nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas

Thomas Schäfer, Derek A. Teaney

Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity η to entropy density s in units of ℏ/ k B is bounded by a constant. Here, ℏ is Planck's constant and k B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that η/ s ⩾ ℏ/(4π k B ). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of η/ s that are smaller than ℏ/ k B . These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.

arXiv:0904.3107•Reports on Progress in Physics•Nov 12, 2009•437 citations

Shear viscosity in a superfluid cold Fermi gas at unitarity

Massimo Mannarelli, Cristina Manuel, Laura Tolós

We analyze the contributions of Nambu-Goldstone modes to the shear viscosity of a superfluid atomic Fermi gas close to unitarity. We show that the low temperature experimental values of the shear viscosity to entropy ratio, $η/s$, are reproduced considering an effective shear viscosity which takes into account the collisions among Nambu-Goldstone bosons and the finite size of the optical trap. We predict that, for $T \lesssim 0.1 T_F$, $η/s$ should correlate with the size of the trap and linearly decrease with decreasing temperature. For $T \gtrsim 0.1 T_F$, we find agreement with the experimental data assuming that the Nambu-Goldstone modes have an anomalous dispersion law.

arXiv:1201.4006•Jan 19, 2012•7 citations

Shear viscosity and damping for a Fermi gas in the unitarity limit

Georg M. Bruun, H. Smith

The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.

arXiv:cond-mat/0612460•Physical Review A•Apr 17, 2007•103 citations

Searching for perfect fluids: quantum viscosity in a universal Fermi gas

C Cao, Ethan Elliott, H Wu +1 more

We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T . We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏ n is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.

arXiv:1105.2496•New Journal of Physics•Jul 21, 2011•44 citations
We extract the shear viscosity to entropy density ratio \ensuremathη/s\ensuremath{\eta}/s\ensuremathη/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 \ensuremathη/s\ensuremath{\eta}/s\ensuremathη/s is roughly equal to 1/2 in units of \ensuremathℏ/kB\ensuremath{\hbar}/{k}_{B}\ensuremathℏ/kB​. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound 1/(4\ensuremathπ)1/(4\ensuremath{\pi})1/(4\ensuremathπ) than any other known liquid.
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 $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.
Eighty years ago Eyring proposed that the shear viscosity of a liquid, ηηη, has a quantum limit η≳nℏη\gtrsim n\hbarη≳nℏ where nnn 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 ηs≥ℏ4πkB\fracη{s}\geq \frac{\hbar}{4πk_{B}}sη​≥4πkB​ℏ​ for the ratio between the shear viscosity and the entropy density, sss. 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 3^{3}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/T21/T^{2}1/T2 dependence, where TTT is the temperature. With increasing temperature and interaction strength UUU 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 3^{3}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.
Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity η to entropy density s in units of ℏ/ k B is bounded by a constant. Here, ℏ is Planck's constant and k B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that η/ s ⩾ ℏ/(4π k B ). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of η/ s that are smaller than ℏ/ k B . These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.
We analyze the contributions of Nambu-Goldstone modes to the shear viscosity of a superfluid atomic Fermi gas close to unitarity. We show that the low temperature experimental values of the shear viscosity to entropy ratio, η/sη/sη/s, are reproduced considering an effective shear viscosity which takes into account the collisions among Nambu-Goldstone bosons and the finite size of the optical trap. We predict that, for T≲0.1TFT \lesssim 0.1 T_FT≲0.1TF​, η/sη/sη/s should correlate with the size of the trap and linearly decrease with decreasing temperature. For T≳0.1TFT \gtrsim 0.1 T_FT≳0.1TF​, we find agreement with the experimental data assuming that the Nambu-Goldstone modes have an anomalous dispersion law.
The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T . We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏ n is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.