We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity, the bulk viscosity, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/(4 pi), with s the entropy density, has significant effects, as expected based on other studies. Introducing a nonzero bulk viscosity also has significant effects. In fact, if the bulk viscosity peaks near the crossover temperature Tc to the degree indicated by recent lattice calculations in QCD without quarks, it can make the fluid cavitate -- falling apart into droplets. It is interesting to see a hydrodynamic calculation predicting its own breakdown, via cavitation, at the temperatures where hadronization is thought to occur in ultrarelativistic heavy ion collisions.
Cavitation and thermal photon production in relativistic heavy ion collisions
我们利用一维助推不变的二阶相对论流体力学研究了热光子产生率，以寻找合适的能量密度和温度随时间的演化。体粘滞效应和非理想状态方程的考虑方式与最近的格点量子色动力学估计一致。结果表明，\textit{non-ideal}气体状态方程，即膨胀等离子体的$ε-3 P \neq 0$行为，在相变点附近是很重要的，它能显著地减慢流体动力学膨胀，从而提高光子产生率。包括体积粘度也可能对流体动力学演化有类似的影响。然而，体积粘度的影响被证明是显着低于\textit{non-ideal}气体状态方程。我们还分析了有趣的现象，体积粘度引起的空化的流体动力学描述无效。结果表明，忽略空化现象会导致对光子通量的严重高估。有人认为，这一特点可能是相关的研究相对论性重离子碰撞中的空化签名。
Background: The near-equilibrium properties of a QCD plasma can be encoded into transport coefficients such as bulk and shear viscosity. In QCD, the ratio of these transport coefficients to entropy density, $ζ/s$ and $η/s$, depends non-trivially on the plasma's temperature. Purpose: We show that in a 0+1D boost-invariant fluid, a temperature-dependent $ζ/s(T)$ or $η/s(T)$ can be described by an equivalent effective viscosity $\left\langle ζ/s \right\rangle_{\textrm{eff}}$ or $\left\langle η/s \right\rangle_{\textrm{eff}}$. We extend the concept of effective viscosity in systems with transverse…
We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken …
We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are able to identify an attractor solution that controls a transition from a free streaming fixed point to a hydrodynamic fixed point. In particular, this attractor solution provides a renormalization of the effective value of the shear viscosity to entropy density ratio, $η/s$, taking into account off-equilibrium effects.
A numerical algorithm for the implementation of anisotropic distributions in the frame of the relativistic Boltzmann equation is presented. The implementation relies on the expansion of the Romatschke-Strickland distribution with respect to orthogonal polynomials, which is evolved using the lattice Boltzmann algorithm. The validation of our proposed scheme is performed in the context of the one-dimensional boost invariant expansion (Bjorken flow) at various values of the ratio $η/ s$ of the shear viscosity to the entropy density. This study is limited to the case of massless particles obeying …
We present an estimate of the behaviour of the shear and bulk viscosity coefficients when the QCD critical point is approached from the hadronic side, describing hadronic matter within the statistical bootstrap model (SBM) of strong interactions. The boostrap model shows critical behavior near the quark-hadron transition temperature if the parameter characterizing the degeneracy of Hagedorn states is properly chosen. We calculate the critical exponents and amplitudes of relevant thermodynamic quantities near the QCD critical point and combine them with an Ansatz for the shear and bulk viscosit…
We study the effect of anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions. We use Glauber model to generate initial conditions and ignore hydrodynamic expansion in the transverse direction. We employ Beer-Lambert law to allow for the transmittance of produced hadrons in the medium and calculate the anisotropy generated due to the suppression of particles traversing through the medium. In order to separate non-flow contribution due to surface bias effects, we ignore hydrodynamic expansion in the transverse direction and consider purely longitudinal boost-invarian…
We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward…
