Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics

Abstract

Within the framework of relativistic fluctuating hydrodynamics we compute the contribution of thermal fluctuations to the effective infrared shear viscosity of a conformal fluid, focusing on quadratic (in fluctuations), second order (in velocity gradients) terms in the conservation equations.Our approach is based on the separation of hydrodynamic fields in soft and ultrasoft sectors, in which the effective shear viscosity arises due to the action of the soft modes on the evolution of the ultrasoft ones. We find that for a strongly coupled fluid with small shear viscosity-toentropy ratio η/s the contribution of thermal fluctuations to the effective shear viscosity is small but significant. Using realistic estimates for the strongly coupled quark-gluon plasma created in heavy ion collisions, we find that for η/s close to the AdS/CFT lower bound 1/(4π) the correction is positive and at most amounts to 10% in the temperature range 200-300 MeV, whereas for larger values η/s ∼ 2/(4π) the correction is negligible. For weakly coupled theories the correction is very small even for η/s = 0.08 and can be neglected.

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

“…Diagrammatic methods are discussed by a number of authors, for example in [14][15][16]. Our work closely follows a recent study of fluctuations in relativistic fluids, see [17,18], the recent review [19], and the related work in [20].…”

Hydrodynamic tails and a fluctuation bound on the bulk viscosity

“…In that case loop diagrams similar to the graphs studied in this work lead to an enhancement of the bulk viscosity near the critical point. Another important problem is the study of fluctuations in relativistic fluids, see [6,10,46,47]. In that case it has been conjectured that the quark gluon plasma phase transition has a critical end point which is in the universality class of model H [26,48], and that critical fluctuations can be observed in the relativistic heavy ion collisions [49].…”

Viscosity of an ideal relativistic quantum fluid: A perturbative study

“…In this regime [15][16][17] show that backreaction is not necessarily negligible. An additional problem is that [16,17] compare the macroscopic viscosity with the microscopic entropy.…”

“…In this regime [15][16][17] show that backreaction is not necessarily negligible. An additional problem is that [16,17] compare the macroscopic viscosity with the microscopic entropy. To estimate a fully macroscopic =s with the approach of [16], one would need to (i) estimate the contribution to the entropy density resulting from an equilibrated ''gas of sound waves,'' and (ii) take the sound-sound interactions fully into account while calculating viscosity.…”