Phase transitions and perfectness of fluids in weakly coupled real scalar field theories

Abstract

We calculate the ratio η/s, the shear viscosity (η) to entropy density (s), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of the η/s behaviors agree with the empirical observations in atomic and molecular systems such as H2O, He, N, and all the matters with data available in the NIST database. 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 clarify some issues regarding counterexamples of the conjectured universal bound η/s ≥ 1/4π found in Refs. [16,17].

Transport coefficients ofO(N)scalar field theories close to the critical point

“…Kinetic approaches employed for computing the transport coefficients (see e.g. [38,39] and a discussion in Ref. [40]) rely heavily on Boltzmann-like approximations, which take only the single particle distribution into account and neglect higher order correlations.…”

Minimum shear viscosity over entropy density at phase transition?—A counterexample

“…It is also seen in cold unitary fermi gases [23], in H 2 O, N, and He and in all the matters with data available in the NIST database [20,22,24]. Theoretically, these behaviors can be reproduced in controlled calculations of weakly interacting real scalar field theories [25].…”

“…There is no interaction between the two fields. The advantage of this model is that its η/s can be computed reliably as in [25] because of the small couplings [27]. Other counterexamples have been asserted previously in literature.…”

“…The η/s of cases I and II are well studied in [25] and we follow the treatment there. λ and µ 2 i are renormalized quantities and the counterterm Lagrangian is not shown.…”

“…The first one is to study strongly interacting systems because strong interaction generally implies small η/s. The second clue can be found in a large class of systems where η/s goes to a local minimum near the phase transition temperature (T c ) [20,21,25]. In particular, η/s develops a cusp(jump) at T c for a second(first) order phase transition and a smooth local minimum for a cross over.…”