Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas

TL;DR

This work analyzes nearly perfect fluids by focusing on the shear viscosity to entropy density ratio, η/s, across three key quantum fluids: liquid helium, unitary ultracold Fermi gases, and the quark–gluon plasma. It surveys three major theoretical frameworks—kinetic theory for quasi-particles, holographic methods via AdS/CFT for strongly coupled regimes, and lattice/linear-response approaches—to connect microscopic dynamics with macroscopic transport. The review highlights a spectrum of results: η/s approaches the proposed universal bound 1/(4π) in strong coupling, with experimental and lattice data supporting very low viscosities in the QGP and cold atoms, while kinetic theory explains higher-κ and diffusion behavior in weakly coupled or gapped regimes. Collectively, these insights illuminate how nature achieves almost perfect fluidity and guide ongoing efforts to unify descriptions of transport from quasi-particles to holographic duals, with implications for both fundamental theory and heavy-ion phenomenology.

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 eta to entropy density s in units of hbar/k_B is bounded by a constant. Here, hbar 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 eta/s is greater or equal to hbar/(4 pi 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 eta/s that are smaller than hbar/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.

Figures (11)

• Figure 1: Entropy density in units of the Stefan-Boltzmann value for pure gauge QCD and ${\cal N}=4$ supersymmetric QCD. The left panel shows the entropy density of pure gauge QCD as a function of $T/T_c$. The grey band is the lattice result. The solid lines show a resummed QCD calculation Blaizot:2003tw. The different lines correspond to different choices for a non-perturbative parameter $c_\Lambda$. The dashed lines mark an error band determined by variations in the QCD renormalization scale. The right panel shows the entropy density of SUSY QCD as a function of the 't Hooft coupling $\lambda$. The curves are labeled as in the left panel.
• Figure 2: Leading order processes that contribute to the shear viscosity of the Fermi gas in the unitarity limit at low temperature (Fig. a) and high temperature (Fig. b). Dashed lines are phonon propagators and solid lines are fermion propagators.
• Figure 3: Leading order processes that contribute to the shear viscosity of a pure gluon plasma. The coefficient $k$ defined in equ. (\ref{['eta_qcd']}) is determined by the $t$-channel diagram. The full leading order result, including the coefficient $\mu^*$, requires the remaining diagrams, as well as gluon bremsstrahlung from the external legs (not shown).
• Figure 4: Shear and bulk viscosity to entropy density ratio in QCD (left panel) and ${\cal N}=4$ supersymmetric Yang-Mills theory (right panel). The left panel shows the shear and bulk viscosity to entropy density ratio in QCD with $N_f=3$ flavors as a function of the strong coupling constant $\alpha_s$, from Arnold:2006fz. The right panel shows the ratio $\eta/s$ in ${\cal N}=4$ SUSY Yang Mills theory as a function of the 't Hooft coupling $\lambda= g^2N_c$. The solid line shows the weak coupling result, the dotted line is an extrapolation of the weak coupling result to the strong coupling regime, the dashed lined is $\lambda\to\infty$ result from the AdS/CFT correspondence, and dash-dotted line is the leading correction to the strong coupling result, from Huot:2006ys.
• Figure 5: Spectral function $\rho^{xyxy}(\omega,{\bf k}\! =\! 0)$ associated with the correlation function of the $xy$ component of the energy momentum tensor. The spectral function is normalized to entropy density $s$. Left panel (Fig. (a)): Schematic picture of the spectral density in weak coupling QCD or SUSY Yang Mills theory Aarts:2002ccMoore:2008ws. Right panel (Fig. (b)): Spectral density in strong coupling SUSY Yang-Mills theory calculated using the AdS/CFT correspondence, from Teaney:2006nc.