Progress of Theoretical Physics Supplement No. 174, 2008 145 Phase Transitions and the Perfectness of Fluids Jiunn-Wei Chen ∗) Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617 We calculate the ratio η/s, the shear viscosity (η) to entropy density (s), which charac- terizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The resulting η/s behaviors agree with the empirical observations in atomic and molecular systems such as H 2 O, He and N. These behaviors are expected to be the same in N component scalar theories with an O(N ) symmetry. We speculate these η/s behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clar- ify some issues regarding counterexamples of the conjectured universal bound η/s ≥ 1/4π found in [T. D. Cohen, Phys. Rev. Lett. 99 (2007), 021602; hep-th/0702136. A. Cherman, T. D. Cohen and P. M. Hohler, arXiv:0708.4201. A. Dobado and F. J. Llanes-Estrada, Eur. Phys. J. C 51 (2007), 913; hep-th/0703132]. Quantum chromodynamics (QCD) is believed to undergo rapid transitions from hadronic phases to a quark-gluon plasma (QGP) phase at high temperature T and to quark matter phases at high quark chemical potential μ (see 1)–3) for reviews). Lattice results show that the phase transition of the hadronic matter to QGP at finite T with μ = 0 is likely a crossover. 4) At finite μ and T = 0, there is no reliable lattice result due to the severe fermion sign problem. However, arguments based on a variety of models show that the phase transition is of first-order. This first-order phase transition turns into a crossover at smaller μ and finite T at the QCD critical end-point (CEP). 5) There are lots of interests in the CEP. Recently, it was proposed to probe the CEP by using the ratio of shear viscosity η to the entropy density s of QCD. 6) Shear viscosity η characterizes how strongly particles interact and move collec- tively in a many-body system. In general, the stronger the interparticle interaction, the smaller the shear viscosity (here η is normalized by the density). It was con- jectured 7) that no matter how strong the particle interaction is, η/s has a universal minimum bound 1/4π in any system. This bound is motivated by the uncertainty principle and is found to be saturated for a large class of strongly interacting quan- tum field theories whose dual descriptions in string theory involve black holes in anti-de Sitter space. 7) There are two important questions regarding this conjecture. The first one is: Is this η/s bound truly universal? By definition, there is no proof of this conjecture yet. From experimental observations, the bound is well satisfied in matters like H 2 O, N and superfluid He. 7) For cold fermionic atoms with an infinite scattering length (the unitarity limit), the bound is satisfied but η/s is close to the bound near the phase transition temperature T c . 8) Similar behavior is found for QCD at μ = 0. 9), 10) Relativistic heavy ion collisions (RHIC) 11)–14) and lattice computations ∗) E-mail: jwc@phys.ntu.edu.tw Downloaded from https://academic.oup.com/ptps/article-abstract/doi/10.1143/PTPS.174.145/1934893 by guest on 05 June 2020