One of the most striking results from the Relativistic Heavy Ion Collider is the strong elliptic flow. This review summarizes what is observed and how these results are combined with reasonable theoretical assumptions to estimate the shear viscosity of QCD near the phase transition. A data comparison with viscous hydrodynamics and kinetic theory calculations indicates that the shear viscosity to entropy ratio is surprisingly small, $η/s < 0.4$. The preferred range is $η/s \simeq (1\leftrightarrow 3) \times 1/4π$.
A new formulation of (3+1)-dimensional anisotropic hydrodynamics is presented that accounts nonperturbatively for the large longitudinal-transverse pressure anisotropy and bulk viscous pressure in heavy-ion collisions. The initialization of the anisotropic hydrodynamic stage is discussed, and a comparison to standard viscous hydrodynamics for (0+1)- dimensional Bjorken expansion is presented.
We calculate the viscous pressure tensor of the quark-gluon plasma in strong magnetic field. It is azimuthally anisotropic and is characterized by five shear viscosity coefficients, four of which vanish when the field strength eB is much larger than the plasma temperature squared. We argue, that the azimuthally anisotropic viscous pressure tensor generates the transverse flow with asymmetry as large as 1/3, even not taking into account the collision geometry. We conclude, that the magnitude of the shear viscosity extracted from the experimental data ignoring the magnetic field must be underest…
Due to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until $O(1)$\,fm/$c$ after the collision. To address this one often introduces a pre-hydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the pre-hydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopic…
The second order Israel-Stewart-M$\ddot{u}$ller relativistic hydrodynamics has been applied to study the effects of causality on the acoustic oscillation in relativistic fluid. Causal dispersion relations have been derived with non-vanishing shear viscosity, bulk viscosity and thermal conductivity at non-zero temperature and chemical potential. These relations have been used to investigate the fluidity of Quark Gluon Plasma (QGP) at finite temperature ($T$). Results of the first order dissipative hydrodynamics have been obtained as limiting case of the second order theory. The effects of the c…
Relativistic Heavy Ion Collisions: Viscous Hydrodynamic Simulations and Final State Interactions
在这篇论文中，我介绍了相对论性重离子碰撞，并描述了理解它们的理论方法--特别是粘性流体动力学模拟和末态相互作用的研究。对相对论重离子对撞机（RHIC）上成功的理想流体动力学模型进行了推广，并进行了粘性流体动力学模拟。这是通过利用最近导出的完全共形不变的二阶相对论粘性流体动力学方程。给出了sqrt{sNN}=200 GeV Au+Au RHIC碰撞中多重数、径向流和椭圆流的计算结果，并给出了我们的流体动力学模型与实验数据相一致的剪切粘滞率与熵密度之比η/s的范围。此外，在大型强子对撞机（LHC）计划的sqrt{s_NN}=5.5 TeV Pb+Pb和sqrt{s}=14 TeV p+p碰撞进行了模拟。与顶能RHIC碰撞相比，Pb+Pb碰撞的椭圆流系数v_2预计要大10%，而质子碰撞的椭圆流系数v_2预计为零，除非eta/s < 0.08。最后，在扭曲波发射函数（DWEF）模型中研究了末态相互作用。本文对DWEF模型作了进一步的研究，并计算了π光学势形式的末态相互作用对椭圆流系数v_2的影响在~20%水平。
The mixture of quark and gluon fluids is studied in a one-dimensional boost-invariant setup using the set of relativistic kinetic equations treated in the relaxation time approximation. Effects of a finite quark mass, non-zero baryon number density, and quantum statistics are discussed. Comparisons between the exact kinetic-theory results and anisotropic hydrodynamics predictions are performed and a very good agreement between the two are found.
The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with the non-extensive equation of state. We have shown that the equations, describing the propagation of nonlinear waves under such situation are KdV-type (Korteweg-De Vries). Apart from their preserved solitonic behaviour the dissipative nature of these waves are also observed. The waves with larger amplitude and width dissipate less and propagate faster and these waves deplete more for both smaller values of Tsall…
The drag and diffusion coefficients are studied within the framework of Fokker-Planck dynamics for the case of a charm quark propagating in an expanding quark-gluon plasma. The space-time evolution of the nuclear matter created in the relativistic heavy-ion collision is modelled using MUSIC, a 3+1 D relativistic viscous hydrodynamic approach. The effect of viscous corrections to the heavy quark transport coefficients is explored by considering scattering processes with thermal quarks and gluons in the medium. It is observed that the momentum diffusion of the heavy quarks is sensitive to the sh…
We extend our hybrid model HydHSD by taking into account shear viscosity within the Israel-Stewart hydrodynamics. The influence of different forms of $π^{μν}$ constraints on observables is analyzed. We show that the form of the corresponding condition plays an important role for the sensitivity of viscous hydrodynamics to the ratio of shear viscosity to the entropy density, $η/s$. It is shown that the constraint used in the vHLLE model, results in most sensitivity of rapidity distributions and transverse momentum spectra to a change of the $η/s$ ratio; however, their applicability for large va…
We study the response function which describes the evolution of energy density induced by an initial disturbance for a Bjorken-expanding quark-gluon plasma (QGP). We compare the results from solving linearized Boltzmann equation under the relaxation time approximation with those from viscous hydrodynamics. While in long time limit the response becomes hydrodynamics, the non-hydrodynamic response is important at intermediate times when excitations of wavelength larger than the inverse of the relaxation time $1/τ_{R}$ are not fully damped. Therefore observables sensitive to the jet-induced mediu…
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）
We study the theory of relativistic viscous hydrodynamics introduced in arXiv:1109.0985 and arXiv:1907.12695, which provided a causal and stable first-order theory of relativistic fluids with viscosity in the case of barotropic fluids. The local well-posedness of its equations of motion has been previously established in Gevrey spaces. Here, we improve this result by proving local well-posedness in Sobolev spaces.
We study the properties of quarkonia inside a bulk-viscous quark gluon plasma. The non-equilibrium nature of the medium is encoded in the deformed distribution functions of thermal quarks and gluons, with which we compute the dielectric permittivity within the hard thermal loop approximation at one-loop. The modified dielectric permittivity is used to calculate the in-medium heavy quark potential, and using the potential we compute spectral functions, which reflect the physical properties of heavy quarkonia. We discuss how the bulk viscous effect influences quantities such as binding energies …
