The recently formulated framework of anisotropic and dissipative hydrodynamics (ADHYDRO) is used to describe non-boost-invariant motion of the fluid created at the early stages of heavy-ion collisions. Very strong initial asymmetries of pressure are reduced by the entropy production processes. By the appropriate choice of the form of the entropy source we can reproduce realistic scenarios for the isotropization expected in heavy-ion collisions. Our previous results are generalized by including the realistic equation of state as the limit of the isotropization processes.
Kinetic and hydrodynamic models describing early stages of relativistic heavy-ion collisions are discussed. We emphasise the role of the shear-bulk coupling for the correct determination of the time dependence of the bulk viscous pressure.
We introduce a new framework of highly-anisotropic hydrodynamics that includes dissipation effects. Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid. With a simple ansatz for the entropy source obeying general physical requirements, we are led to a non-linear equation describing the time evolution of the anisotropy in purely-longitudinal boost-invariant systems. Matter that is initially highly anisotropic approaches naturally the regime of the perfect fluid. Thus, the resulting evolution agrees with the expect…
The quark gluon plasma generated in ultrarelativistic heavy ion collisions may possess sizable momentum-space anisotropies that cause the longitudinal and transverse pressures in the local rest frame to be significantly different. We review recent attempts to derive a dynamical framework that can reliably describe systems that possess a high degree of momentum-space anisotropy. The dynamical framework that has been developed can describe the evolution of the quark gluon plasma ranging from the longitudinal free-streaming limit to the ideal hydrodynamical limit.
In this paper we present a method to improve the description of 0+1 dimensional boost invariant dissipative dynamics in the presence of large momentum-space anisotropies. We do this by reorganizing the canonical hydrodynamic expansion of the distribution function around a momentum-space anisotropic ansatz rather than an isotropic equilibrium one. At leading order the result obtained is two coupled ordinary differential equations for the momentum-space anisotropy and typical momentum of the degrees of freedom. We show that this framework can reproduce both the ideal hydrodynamic and free stream…
Tensors describing boost-invariant and cylindrically symmetric expansion of a relativistic dissipative fluid are decomposed in a suitable chosen basis of projection operators. This leads to a simple set of scalar equations which determine the fluid behavior. As special examples, we discuss the case of the Israel-Stewart theory and the model of highly-anisotropic and strongly-dissipative hydrodynamics ADHYDRO. We also introduce the matching conditions between the ADHYDRO description suitable for the very early stages of heavy-ion collisions and the Israel-Stewart theory applicable for later sta…
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade descri…
The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during the early stages of heavy-ion collisions, is analyzed within the frameworks of viscous and anisotropic hydrodynamics. We neglect transverse dynamics and assume homogeneous conditions in the transverse plane but, differently from Bjorken expansion, we relax longitudinal boost invariance in order to study the rapidity dependence of various hydrodynamical observables. We compare the results obtained using several formulations of second-order viscous hydrodynamics with a recent approach to aniso…
We compute dilepton production from the deconfined phase of the quark-gluon plasma using leading-order (3+1)-dimensional anisotropic hydrodynamics. The anisotropic hydrodynamics equa- tions employed describe the full spatiotemporal evolution of the transverse temperature, spheroidal momentum-space anisotropy parameter, and the associated three-dimensional collective flow of the matter. The momentum-space anisotropy is also taken into account in the computation of the dilepton production rate, allowing for a self-consistent description of dilepton production from the quark-gluon plasma. For our…
A significant fraction of the changes in momentum distributions induced by dissipative phenomena in the description of the fluid fireball created in ultrarelativistic heavy-ion collisions actually take place when the fluid turns into individual particles. We study these corrections in the limit of a low freeze-out temperature of the flowing medium, and we show that they mostly affect particles with a higher velocity than the fluid. For these, we derive relations between different flow harmonics, from which the functional form of the dissipative corrections could ultimately be reconstructed fro…
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 …
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dy…
We study the non-boost-invariant evolution of a quark-gluon plasma subject to large early-time momentum-space anisotropies. Rather than using the canonical hydrodynamical expansion of the distribution function around an isotropic equilibrium state, we expand around a state which is anisotropic in momentum space and parameterize this state in terms of three proper-time and spatial-rapidity dependent parameters. Deviations from the Bjorken scaling solutions are naturally taken into account by the time evolution of the spatial-rapidity dependence of the anisotropic ansatz. As a result, we obtain …
In this review, we present the motivation for using relativistic anisotropic hydrodynamics to study the physics of ultrarelativistic heavy-ion collisions. We then highlight the main ingredients of the 3+1D quasiparticle anisotropic hydrodynamics model and present phenomenological comparisons with experimental data at different collision energies. These comparisons show that anisotropic hydrodynamics can describe many bulk observables of the quark-gluon plasma.
A recently formulated framework of highly-anisotropic and strongly-dissipative hydrodynamics (ADHYDRO) is used to describe the evolution of matter created in ultra-relativistic heavy-ion collisions. New developments of the model contain: the inclusion of asymmetric transverse expansion (combined with the longitudinal boost-invariant flow) and comparisons of the model results with the RHIC data, which have become possible after coupling of ADHYDRO with THERMINATOR. Various soft-hadronic observables (the transverse-momentum spectra, the elliptic flow coefficient v_2, and the HBT radii) are calcu…
We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained …
We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)-dimensional boost invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte-Carlo Glauber initial conditions. For this purpose we have developed two numeric…
A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy-momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe …
We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain non-hydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from…
We study anomalous magnetohydrodynamics in a longitudinal boost invariant Bjorken flow with constant anisotropic electric conductivities as outlined in Ref. [1]. For simplicity, we consider a neutral fluid and a force-free magnetic field in the transverse direction. We derived analytic solutions of the electromagnetic fields in the laboratory frame, the chiral density, and the energy density as functions of proper time.
Non-additive generalisation of relativistic anisotropic anisotropic hydrodynamics is described. In the particular case of 0+1 boost-invariant hydrodynamics additional entropy production due to non-additivity is calculated.
We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter $q$. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including $q$. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with r…
We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hy…
The effective low-energy late-time description of many body systems near thermal equilibrium provided by classical hydrodynamics in terms of dissipative transport phenomena receives important corrections once the effects of stochastic fluctuations are taken into account. One such physical effect is the occurrence of long-time power law tails in correlation functions of conserved currents. In the hydrodynamic regime $\vec{k} \rightarrow 0$ this amounts to non-analytic dependence of the correlation functions on the frequency $ω$. In this article, we consider a relativistic fluid with a conserved…
Dissipative relativistic fluid-dynamical descriptions of the extended fireball formed in high-energy heavy-ion collisions are quite successful, yet require a prescription for converting the fluid into particles. We present arguments in favour of using a locally anisotropic momentum distribution for the particles emitted from the fluid, so as to smooth out discontinuities introduced by the usual conversion prescriptions. Building on this ansatz, we investigate the effect of the asymmetry on several observables of heavy ion physics.
Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing proc…
In this contribution we study the effects of three transport coefficients of dissipative hydrodynamics on thermal dilepton anisotropic flow observables. The first two transport coefficients investigated influence the overall size and growth rate of shear viscous pressure, while the last transport coefficient governs the magnitude of net baryon number diffusion in relativistic dissipative fluid dynamics. All calculations are done using state-of-the-art 3+1D hydrodynamical simulations. We show that thermal dileptons are sensitive probes of the transport coefficients of dissipative hydrodynamics.
We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they app…
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high particle number systems give more clear and comprehensive physical descriptions of those systems than purely kinetic approaches, and can be more easily tested experimentally as well as numerically. In particular, we aim at developing a theory that describes both a background non-equilibrium fluid configurations and its perturbations, to be able to account f…
We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor, $τ_π$, to the sound attenuation length, $Γ_s = 4η/3(\varepsilon+P)$, fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solut…
Explicit equations are given for describing the space-time evolution of non-ideal (viscous) relativistic fluids undergoing boost-invariant longitudinal and arbitrary transverse expansion. The equations are derived from the second-order Israel-Stewart approach which ensures causal evolution. Both azimuthally symmetric (1+1)-dimensional and non-symmetric (2+1)-dimensional transverse expansion are discussed. The latter provides the formal basis for the hydrodynamic computation of elliptic flow in relativistic heavy-ion collisions including dissipative effects.
The model assumptions of the recently formulated framework of highly-anisotropic and strongly-dissipative hydrodynamics (ADHYDRO) are analyzed. In particular, we study dependence of numerical results on different forms of the entropy source and compare our approach with other frameworks describing locally anisotropic fluids. We also discuss the effects of different forms of the initial conditions on the process of isotropization.
We present a new derivation of relativistic dissipative hydrodynamic equations, which invokes the second law of thermodynamics for the entropy four-current expressed in terms of the single-particle phase-space distribution function obtained from Grad's 14-moment approximation. This derivation is complete in the sense that all the second-order transport coefficients are uniquely determined within a single theoretical framework. In particular, this removes the long-standing ambiguity in the relaxation time for bulk viscosity thereby eliminating one of the uncertainties in the extraction of the s…
Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor $π^{αβ}$ and derive a novel third-order evolution equation for $π^{αβ}$. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio $η/s$ are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at $τ_0=0.4 fm/c$, the third-order corrections to Israel-Stewart theor…
We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice QCD equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.
Recently formulated model of highly-anisotropic and strongly dissipative hydrodynamics is used in 3+1 dimensions to study behavior of matter produced in ultra-relativistic heavy-ion collisions. We search for possible effects of the initial high anisotropy of pressure on the final soft-hadronic observables. We find that by appropriate adjustment of the initial energy density and/or the initial pseudorapidity distributions, the effects of the initial anisotropy of pressure may be easily compensated and the final hadronic observables become insensitive to early dynamics. Our results indicate that…
The Müller-Israel-Stewart second order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultra-relativistic heavy ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.
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 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 study anisotropic fluid dynamics derived from the Boltzmann equation based on a particular choice for the anisotropic distribution function within a boost-invariant expansion of the fluid in one spatial dimension. In order to close the conservation equations we need to choose an additional moment of the Boltzmann equation. We discuss the influence of this choice of closure on the time evolution of fluid-dynamical variables and search for the best agreement to the solution of the Boltzmann equation in the relaxation-time approximation.
In Molnár et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dy…
We show that in hydrodynamic simulations for relativistic heavy-ion collisions, strong resonance decay calculations can be performed with fewer species of particle resonances while preserving good accuracy in single particle spectra and flow anisotropies. Such partial resonance calculations boost computation efficiency by a factor of 10 which is essential for large scale event-by-event simulations.
The (viscous) anisotropic hydrodynamic approach, especially after perturbative inclusion of all residual viscous terms, has been shown to dramatically outperform viscous hydrodynamics in several simplified situations for which exact solutions exist but which share with realistic expansion scenarios the problem of large dissipative currents. We will report on the present status of applying viscous anisotropic hydrodynamics in a highly efficient simulation of the full three-dimensional quark-gluon plasma. Results from accelerated $3{+}1$-dimensional viscous hydrodynamic simulations using graphic…
Non-equilibrium fluid dynamics derived from the extended irreversible thermodynamics of the causal Müller--Israel--Stewart theory of dissipative processes in relativistic fluids based on Grad's moment method is applied to the study of the dynamics of hot matter produced in ultra--relativistic heavy ion collisions. The temperature, energy density and entropy evolution are investigated in the framework of the Bjorken boost--invariant scaling limit. The results of these second order theories are compared to those of first order theories due to Eckart and to Landau and Lifshitz and those of zeroth…
Using the AdS/CFT correspondence, we compute analytically the late-time behavior of two-point functions, Wilson loops and entanglement entropy in a strongly coupled $\mathcal{N}=4$ super-Yang-Mills plasma undergoing a boost-invariant expansion. We take into account the effects of first order dissipative hydrodynamics and investigate the effects of the (time-dependent) shear viscosity on the various observables. The two-point functions decay exponentially at late times and are unaffected by the viscosity if the points are separated along the transverse directions. For longitudinal separation we…
Based on a 14-moment closure for non-resistive (general-) relativistic viscous plasmas, we describe a new numerical scheme that is able to handle all first-order dissipative effects (heat conduction, bulk and shear viscosities), as well the anisotropies induced by the presence of magnetic fields. The latter is parameterized in terms of a thermal gyrofrequency or, equivalently, a thermal Larmor radius and allows to correctly capture the thermal Hall effect. By solving an extended Israel-Stewart-like system for the dissipative quantities that enforces algebraic constraints via stiff-relaxation, …
