Nearly perfect fluidity

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 h̄/kB is bounded by a constant. Here, h̄ is Planck’s constant and kB 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 h̄/(4πkB). 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 h̄/kB. 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. (Some figures in this article are in colour only in the electronic version) This article was invited by G Baym.