Relativistic Fluid Dynamics in and out of Equilibrium

Abstract

Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions. PrefaceStrictly speaking, the subtitle of this work is somewhat misleading. Considerable progress on relativistic viscous fluid dynamics had been made earlier than 2007 both in the context of theoretical formulations as well as in numerical simulations. However, in particular for simulations of high energy nuclear collisions, typically an unrealistically high degree of symmetry had been assumed, making the resulting dynamics 0+1d or 1+1 dimensional. Only ten years ago, simulations in 2+1d became available, which is the minimum required to simulate the so-called elliptic flow observed in experiments. As one of the groups that first achieved 2+1d relativistic viscous fluid dynamics simulations ten years ago, we took the opportunity to celebrate this anniversary by compiling the present review of the current status of the field. Given the ongoing vibrant research activity on relativistic viscous fluid dynamics as well as continued experimental developments, we fully expect this review to be outdated in a few years. This is of course good news, and we hope it will require a new review subtitled "Twenty Years of Progress" when the time has come.Happy anniversary, relativistic viscous fluid dynamics!

Calculation of anisotropic transport coefficients for an ultrarelativistic Boltzmann gas in a magnetic field within a kinetic approach

“…The time evolution of the correlation functions corresponding to these conductivity coefficients [see Eqs. (24), (25), (27), and (28)] are shown in Fig. 6 and Fig.…”

“…The transport coefficients are important physical quantities characterizing the features of QGP and reflecting the nature of interactions between quarks and gluons. In the last decade, dissipative hydrodynamic models [17][18][19][20][21][22][23][24][25] have played a very important role in extracting the shear and bulk viscosity of QGP from the flow measurements [4,[26][27][28][29][30][31][32][33]. Now it is necessary to develop models based on relativistic magneto-hydrodynamics (MHD) [34,35], in order to study QGP dynamics in the presence of magnetic field [36][37][38][39][40][41][42][43][44][45][46][47].…”

Bulk viscosity and cavitation in heavy ion collisions

“…For conformal systems where the bulk correction vanishes, a model for δf can be derived that correctly reproduces the hydrodynamic energy-momentum tensor and is well behaved even for large shear stresses (cf. [3], section 3.1.5). Similarly, models for δf within the framework of anisotropic hydrodynamics have been proposed that correctly reproduce a non-interacting expanding gas [28].…”

“…Extensive experimental measurements at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) indicate that the QGP value near the crossover temperature region 150 < T < 400 MeV is close to the conjectured bound -for a useful review see Ref. [3,4]. In contrast, less attention has been cast on studies and experimental constraints of bulk viscosity, though it is no less fundamental a property of QGP.…”

Wigner function formalism and the evolution of thermodynamic quantities in an expanding magnetized plasma

“…It is widely believed that at τ 0 ∼ 0.2 fm/c after the collision, the created hot plasma enters a state of local thermal equilibrium. There are strong pieces of evidence that at this stage, the dynamics of the created quark matter is well described by relativistic hydrodynamics (for a recent review see [1] and references therein), that, because of extremely large magnetic fields that are also created in noncentral HIC experiments [2][3][4][5], is to be extended to relativistic MHD [6]. Assuming firstly that the plasma expands uniformly in the longitudinal direction with respect to the beam direction, and secondly that the external magnetic field is aligned perpendicular to the plasma velocity, it was recently possible to extend the well-known 1 + 1-dimensional Bjorken solution of relativistic hydrodynamics [7,8] to the so-called "ideal transverse MHD" [9], and to determine the proper time evolution of the magnetic field after the onset of hydrodynamics.…”