Motivated by the physics of the quark-gluon plasma created in heavy-ion collision experiments, we use holography to study the regime of applicability of various theories of relativistic viscous hydrodynamics. Using the microscopic description provided by holography of a system that relaxes to equilibrium, we obtain initial data with which we perform real-time evolutions in 2+1 dimensional conformal fluids using the first-order viscous relativistic hydrodynamics theory of Bemfica, Disconzi, Noronha and Kovtun (BDNK), BRSSS and ideal hydrodynamics. By initializing the hydrodynamics codes at different times, we can check the constitutive relations and assess the predictive power and accuracy of each of these theories.
Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
Peking University（北京大学）；Ghent University（根特大学）；Universität Bielefeld（比勒费尔德大学）；The Ohio State University（俄亥俄州立大学）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
This is a comment to hep-th/0703243. The paper determined the relaxation time tau_pi of the shear viscous stress for the N=4 SYM from AdS/CFT correspondence. The purpose of this comment is to point out that the value of tau_pi is 3 times larger than their result if one takes into account an additional term in the hydrodynamic equation.
We consider an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for N=4 SYM. We determine the relaxation time in second order viscous hydrodynamics and find that it is around thirty times shorter than weak coupling expectations. We find that the nonsingularity of the dual geometry in the string frame necessitates turning on the dilaton which leads to a nonvanishing expectation value for tr F^2 behaving like tau^(-10/3).
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge conservation. Recently there has been significant interest in understanding the implications of angular momentum conservation for a corresponding hydrodynamic theory. In this work, we examine the key conceptual issues for such a theory in the relativistic regime where the orbital and spin components get entangled. We derive the equations for relativistic visco…
The charged-particle's final state spectrum is derived from an analytic perturbative solution for the relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus colliding systems at RHIC and LHC. Based on both the extracted longitudinal acceleration parameters $λ^{*}$ and a phenomenological description of the $λ^{*}$, the charged-particle's pseudorapidity distributions for $\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state express…
We compute coefficients of two-derivative terms in the hydrodynamic energy momentum tensor of a viscous fluid which has an AdS_D dual with D between 3 and 7. For the case of D=3 we obtain an exact AdS_3 black hole solution, valid to all orders in a derivative expansion, dual to a perfect fluid in 1+1 dimensions.
The solutions of relativistic viscous hydrodynamics for longitudinal expanding fireballs is investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and Euler conservation equations for the viscous fluid are derived in Rindler coordinates with the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the long…
The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to be characterized by a hydrodynamic attractor which has an early-time behavior that is reminiscent of the so-called bottom-up thermalization scenario in heavy-ion collisions. The hydrodynamization times for the two sectors can differ strongly, with details depending on the curve realized on the two-dimensional attractor surface, which might account for differ…
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, r…
We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled N=4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Muelle…
The Quark Gluon Plasma produced in heavy-ion collisions has three relevant conserved charges: baryon number (B), strangeness (S), and electric charge (Q). Here we derive the Israel-Stewart framework for BSQ diffusion coupled to shear and bulk viscosity and the thermodynamic derivatives needed to couple this to a BSQ equation of state. We reproduce a subset of the ${\mathcal{J}}$ terms in the DNMR approach and propose a technique to derive other terms from the maximum entropy principle. Finally, we preform a stability analysis that can be used to constraint transport coefficients in BSQ hydrody…
A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consisten…
A minimum uncertainty state for position and momentum of a fluid element is obtained. We consider a general fluid described by the Navier-Stokes-Korteweg (NSK) equation, which reproduces the behaviors of a standard viscous fluid, a fluid with the capillary action and a quantum fluid, with the proper choice of parameters. When the parameters of the NSK equation is adjusted to reproduce Madelung's hydrodynamic representation of the Schreodinger equation, the uncertainty relation of a fluid element reproduces the Kennard and the Robertson-Schreodinger inequalities in quantum mechanics. The derive…
The second-order hydrodynamic equations for evolution of shear and bulk viscous pressure have been derived within the framework of covariant kinetic theory based on the effective fugacity quasiparticle model. The temperature-dependent fugacity parameter in the equilibrium distribution function leads to a mean field term in the Boltzmann equation which affects the interactions in the hot QCD matter. The viscous corrections to distribution function, up to second-order in gradient expansion, have been obtained by employing a Chapman-Enskog like iterative solution of the effective Boltzmann equati…
Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero …
Space-time evolution and subsequent particle production from minimally viscous ($η/s$=0.08) QGP fluid is studied using the 2nd order Israel-Stewart's theory of dissipative relativistic fluid. Compared to ideal fluid, energy density or temperature evolves slowly in viscous dynamics. Particle yield at high $p_T$ is increased. Elliptic flow on the other hand decreases in viscous dynamics. Minimally viscous QGP fluid found to be consistent with a large number of experimental data.
The first order hydrodynamic evolution equations for the shear stress tensor, the bulk viscous pressure and the charge current have been studied for a system of quarks and gluons, with a non-vanishing quark chemical potential and finite quark mass. The first order transport coefficients have been obtained by solving an effective Boltzmann equation for the grand-canonical ensemble of quasiquarks and quasigluons. We adopted temperature dependent effective fugacity for the quasiparticles to encode the hot QCD medium effects. The non-trivial energy dispersion of the quasiparticles induces mean fie…
We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.
