New Developments in Relativistic Viscous Hydrodynamics

Abstract

Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of applicability, and can be applied to both weakly and strongly coupled systems. In its modern formulation, relativistic viscous hydrodynamics can directly be solved numerically. This has been useful for the problem of ultrarelativistic heavy-ion collisions, and I will review the setup and results of a hydrodynamic description of experimental data for this case. Contents

Nonlinear waves in second order conformal hydrodynamics

“…In the usual RPM method, only terms proportional to σ and σ 2 are kept. However, the linear hydrodynamical modes (18) and (19) show that relaxation effects may appear only in the next order of the usual expansion, i.e., at orderk 3 . For this reason we consider the σ expansion up to O(σ 3 ) terms to study relaxation effects in nonlinear waves.…”

“…For instance, one can use this theory to investigate the evolution of density perturbations in a non-relativistic hadron gas and in a non-relativistic quark gluon plasma. Perturbations are usually studied with the linearization formalism [19,20], which is the simplest way to study small deviations from equilibrium to obtain wave equations, eventually featuring dissipative and relaxation terms. The propagation of perturbations through a QGP has been investigated in several works with the help of a linearized version of the hydrodynamics of perfect fluids and of viscous fluids.…”

The shear channel spectral function in hot Yang-Mills theory

“…This work has been largely motivated by the experimental heavy ion programs taking place at RHIC and the LHC [1,2], which have highlighted the importance of not only understanding the bulk equilibrium properties of the produced matter but also its hydrodynamic behavior. One particularly prominent observation in this direction has been the discovery of the sizable effect that the small, yet finite value of the shear viscosity η has on the flow properties of the plasma [3,4]. Unfortunately, the first principles determination of transport coefficients in an interacting quantum field theory is a notoriously hard problem.…”

On the infrared behavior of the shear spectral function in hot Yang-Mills theory

“…Instead, we will simply walk the reader through the necessary notations and definitions in section 2. After this, we explain the details of the HTL resummation in section 3, and subsequently present and analyze our results in section 4. Section 5 is finally devoted to drawing conclusions, while appendices A-C contain some lengthy definitions and technical details concerning the evaluation of the master sum-integrals encountered.…”

“…[1][2][3][4][5]). Despite the strong experimental and phenomenological motivation, a nonperturbative first principles tool to predict its value is, however, still lacking, even though an extensive amount of work has been devoted to the topic in the weak coupling [6,7], lattice [8][9][10] and gauge/gravity frontiers [11][12][13].…”