© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:0904.3107 · Reports on Progress in Physics

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

Thomas Schäfer, Derek A. Teaney

Published Nov 12, 2009• 437 citations

Abstract

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.

DOI: 10.1088/0034-4885/72/12/126001

Related papers

Fluid Dynamics and Viscosity in Strongly Correlated Fluids

Thomas Schäfer

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.

arXiv:1403.0653•Annual Review of Nuclear and Particle Science•Jul 8, 2014•64 citations

Perfect Fluidity in Atomic Physics

Thomas Schäfer

Experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) have been interpreted in terms of a strongly interacting quark gluon plasma. The strongly interacting plasma is characterized by ``perfect fluidity'', i.e. a ratio of shear viscosity to entropy density that saturates a proposed lower bound. In this contribution we explore the possibility that a similar phenomenon takes place in a strongly coupled non-relativistic Fermi liquid in which the scattering length between the Fermions is infinitely large.

arXiv:0707.1504•Jul 10, 2007•0 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 in a high-temperature superconductor

J. D. Rameau, Theodore James Reber, H. B. Yang +4 more

Perfect fluids are characterized as having the smallest ratio of shear viscosity to entropy density, $\ensuremath{\eta}/s$, consistent with quantum uncertainty and causality. So far, nearly perfect fluids have only been observed in the quark-gluon plasma and in unitary atomic Fermi gases, exotic systems that are amongst the hottest and coldest objects in the known universe, respectively. We use angle resolved photoemission spectroscopy to measure the temperature dependence of an electronic analog of $\ensuremath{\eta}/s$ in an optimally doped cuprate high-temperature superconductor, finding it too is a nearly perfect fluid around, and above, its superconducting transition temperature ${T}_{c}$.

arXiv:1409.5820•Physical Review B•Oct 13, 2014•36 citations

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

Thomas Schäfer

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.

arXiv:cond-mat/0701251•Physical Review A•Dec 20, 2007•106 citations

Hydrodynamics of unitary Fermi gases

Ryan E. Young

Unitary fermi gases have been widely studied as they provide a tabletop archetype for research on strongly coupled many body systems and perfect fluids. Research into unitary fermi gases can provide insight into may other strongly interacting systems including high temperature superconductor, quark-gluon plasmas, and neutron stars. Within the unitary regime, the equilibrium transport coefficients and thermodynamic properties are universal functions of density and temperature. Thus, unitary fermi gases provide a archetype to study nonperturbative many-body physics, which is of fundamental significance and crosses several fields.\nThis thesis reports on two topics regarding unitary fermi gases. A recent string theory conjecture gives a lower bound for the dimensionless ratio of shear viscosity of entropy, η=s ≥ 4πℏ =kb. Unitary fermi gases are a candidate for prefect fluids, yet η=s is well above the string theory bound. Using a stochastic formulation of hydrodynamics, we calculate a lower bound for this ratio accounting for the momentum dissipation from fluctuations. This lower bound is in good agreement with both theoretical and experimental results.\nThe second question addressed is the simulation of elliptic flow. Elliptic flow, first observed in 2002, is a characteristic of strongly coupled systems and has been studied in both quark-gluon plasmas and unitary fermi gases. As such, simulations of these systems are of interest. We test a variety of lattice Boltzmann models and compare the simulation results to the theoretical and experimental findings.

•Jan 1, 2013•0 citations

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 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.

Experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) have been interpreted in terms of a strongly interacting quark gluon plasma. The strongly interacting plasma is characterized by ``perfect fluidity'', i.e. a ratio of shear viscosity to entropy density that saturates a proposed lower bound. In this contribution we explore the possibility that a similar phenomenon takes place in a strongly coupled non-relativistic Fermi liquid in which the scattering length between the Fermions is infinitely large.

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.

Perfect fluids are characterized as having the smallest ratio of shear viscosity to entropy density, $\ensuremath{\eta}/s$, consistent with quantum uncertainty and causality. So far, nearly perfect fluids have only been observed in the quark-gluon plasma and in unitary atomic Fermi gases, exotic systems that are amongst the hottest and coldest objects in the known universe, respectively. We use angle resolved photoemission spectroscopy to measure the temperature dependence of an electronic analog of $\ensuremath{\eta}/s$ 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}

.

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.

Unitary fermi gases have been widely studied as they provide a tabletop archetype for research on strongly coupled many body systems and perfect fluids. Research into unitary fermi gases can provide insight into may other strongly interacting systems including high temperature superconductor, quark-gluon plasmas, and neutron stars. Within the unitary regime, the equilibrium transport coefficients and thermodynamic properties are universal functions of density and temperature. Thus, unitary fermi gases provide a archetype to study nonperturbative many-body physics, which is of fundamental significance and crosses several fields.\nThis thesis reports on two topics regarding unitary fermi gases. A recent string theory conjecture gives a lower bound for the dimensionless ratio of shear viscosity of entropy, η=s ≥ 4πℏ =kb. Unitary fermi gases are a candidate for prefect fluids, yet η=s is well above the string theory bound. Using a stochastic formulation of hydrodynamics, we calculate a lower bound for this ratio accounting for the momentum dissipation from fluctuations. This lower bound is in good agreement with both theoretical and experimental results.\nThe second question addressed is the simulation of elliptic flow. Elliptic flow, first observed in 2002, is a characteristic of strongly coupled systems and has been studied in both quark-gluon plasmas and unitary fermi gases. As such, simulations of these systems are of interest. We test a variety of lattice Boltzmann models and compare the simulation results to the theoretical and experimental findings.