Dissipative dynamics of highly anisotropic systems

Physical Review Letters

We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph et al. [1] and measurements of the equation of state by Ku et al. [2]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n| Tc = 0.41 ± 0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above Tc with η/s| min = 0.50 ± 0.10.

Physical Review D

In the early stages of heavy-ion collisions, the hot QCD matter expands more longitudinally than transversely. This imbalance causes the system to become rapidly colder in the longitudinal direction and a local momentum anisotropy appears. In this paper, we study the heavy-quarkonium spectrum in the presence of a small plasma anisotropy. We work in the framework of pNRQCD at finite temperature. We inspect arrangements of non-relativistic and thermal scales complementary to those considered in the literature. In particular, we consider temperatures larger and Debye masses smaller than the binding energy, which is a temperature range relevant for presently running LHC experiments. In this setting we compute the leading thermal corrections to the binding energy and the thermal width induced by quarkonium gluo-dissociation.

Physical Review D, 2017

In this paper we address the derivation of causal relativistic hydrodynamics, formulated within the framework of Divergence Type Theories (DTTs), from kinetic theory for spinless particles obeying Fermi-Dirac statistics. The approach leads to expressions for the particle current and energy momentum tensor that are formally divergent, but may be given meaning through a process of regularization and renormalization. We demonstrate the procedure through an analysis of the stability

International Journal of Modern Physics A

We use the dissipative-type theory (DTT) framework to solve for the evolution of conformal fluids in Bjorken and Gubser flows from isotropic initial conditions. The results compare well with both exact and other hydrodynamic solutions in the literature. At the same time, DTTs enforce the Second Law of thermodynamics as an exact property of the formalism, at any order in deviations from equilibrium, and are easily generalizable to more complex situations.

Physical Review C, 2013

We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying different non-equilibrium cases and comparing the exact kinetic-theory results to the second-order viscous hydrodynamics results we find that recent formulations of second-order viscous hydrodynamics agree better with the exact solution than the standard Israel-Stewart approach. Additionally, we find that, given the appropriate connection between the kinetic and anisotropic hydrodynamics relaxation times, anisotropic hydrodynamics provides a very good approximation to the exact relaxation time approximation solution.

Physical Review C, 2013

The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy parameters. The dynamical equations describing such mixtures are derived from kinetic theory with the collisional kernel treated in the relaxation-time approximation. Baryon number conservation is enforced in the quark and anti-quark components of the fluid, but overall parton number non-conservation is allowed in the system. The resulting equations are solved numerically in the (0+1)-dimensional boost-invariant case at zero and finite baryon density.

Physical Review C, 2012

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 early thermalization assumption is not necessary to describe hadronic data, in particular, to reproduce the measured elliptic flow v2. The complete thermalization of matter (local equilibration) may take place only at the times of about 1-2 fm/c, in agreement with the results of microscopic models.

Physical Review C, 2012

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 stages when the system is close to equilibrium.

Physical Review C, 2014

We derive the form of the viscous corrections to the phase-space distribution function due to bulk viscous pressure and shear stress using the iterative Chapman-Enskog method. We then calculate the transport coefficients necessary for the second-order hydrodynamic evolution of the bulk viscous pressure and the shear stress tensor. We demonstrate that the transport coefficients obtained using the Chapman-Enskog method are different than those obtained previously using 14-moment approximation for finite particle mass. Specializing to the case of boost-invariant and transversally homogeneous longitudinal expansion, we show that the transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation compared to results obtained in the 14-moment approximation. Finally, we explicitly confirm that the time evolution of the bulk viscous pressure is significantly affected by its coupling to the shear stress tensor.

Physical Review C, 2014

We compute the temporal evolution of the pressure anisotropy and bulk pressure of a massive gas using second-order viscous hydrodynamics and anisotropic hydrodynamics. We then compare our results with an exact solution of the Boltzmann equation for a massive gas in the relaxation time approximation. We demonstrate that, within second-order viscous hydrodynamics, the inclusion of the full set of kinetic coefficients, particularly the shear-bulk couplings, is necessary to properly describe the time evolution of the bulk pressure. We also compare the results of secondorder hydrodynamics with those obtained using the anisotropic hydrodynamics approach. We find that anisotropic hydrodynamics and second-order viscous hydrodynamics including the shear-bulk couplings are both able to reproduce the exact evolution with comparable accuracy.

Physical Review D, 2015

We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally-symmetric transverse "Gubser" flow using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle distribution function is ellipsoidallysymmetric in the momenta conjugate to the de Sitter coordinates used to parametrize the Gubser flow. We then demonstrate that the SO(3) q symmetry in de Sitter space further constrains the anisotropy tensor to be of spheroidal form. The resulting system of two coupled ordinary differential equations for the de Sitter space momentum scale and anisotropy parameter are solved numerically and compared to a recently obtained exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We show that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches. In addition, we prove that anisotropic hydrodynamics gives the exact solution of the relaxation-time approximation Boltzmann equation in the ideal, η/s → 0, and free-streaming, η/s → ∞, limits.

Physical Review C, 2014

We derive a system of moment-based dynamical equations that describe the 1+1d space-time evolution of a cylindrically symmetric massive gas undergoing boost-invariant longitudinal expansion. Extending previous work, we introduce an explicit degree of freedom associated with the bulk pressure of the system. The resulting form generalizes the ellipsoidal one-particle distribution function appropriate for massless particles to massive particles. Using this generalized form, we obtain a system of partial differential equations that can be solved numerically. In order to assess the performance of this scheme, we compare the resulting anisotropic hydrodynamics solutions with the exact solution of the 0+1d Boltzmann equation in the relaxation time approximation. We find that the inclusion of the bulk degree of freedom improves agreement between anisotropic hydrodynamics and the exact solution for a massive gas.

Physical Review C, 2014

The framework of anisotropic hydrodynamics is generalized to include finite particle masses. Two schemes are introduced and their predictions compared with exact solutions of the kinetic equation in the relaxation time approximation. The first formulation uses the zeroth and first moments of the kinetic equation, whereas the second formulation uses the first and second moments. For the case of one-dimensional boost-invariant expansion, our numerical results indicate that the second formulation yields much better agreement with the exact solutions.

Physical Review C, 2015

A system of equations for anisotropic hydrodynamics is derived that describes a mixture of anisotropic quark and gluon fluids. The consistent treatment of the zeroth, first and second moments of the kinetic equations allows us to construct a new framework with more general forms of the anisotropic phase-space distribution functions than those used before. In this way, the main difficiencies of the previous formulations of anisotropic hydrodynamics for mixtures have been overcome and the good agreement with the exact kinetic-theory results is obtained.

Physical Review C, 2015

We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of boostinvariant and transversally homogeneous longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of massive 0+1d Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation in relaxation-time approximation.

Physical Review C, 2015

We compute the QGP suppression of Υ(1s), Υ(2s), Υ(3s), χ b1 , and χ b2 states in √ sNN = 2.76 TeV Pb-Pb collisions. Using the suppression of each of these states, we estimate the inclusive RAA for the Υ(1s) and Υ(2s) states as a function of Npart, y, and pT including the effect of excited state feed down. We find that our model provides a reasonable description of preliminary CMS results for the Npart-, y-, and pT-dependence of RAA for both the Υ(1s) and Υ(2s). Comparing to our previous model predictions, we find a flatter rapidity dependence, thereby reducing some of the tension between our model and ALICE forward-rapidity results for Υ(1s) suppression.

Physical Review C, 2015

By employing a Chapman-Enskog like iterative solution of the Boltzmann equation in relaxationtime approximation, we derive a new expression for the entropy four-current up to third order in gradient expansion. We show that unlike second-order and third-order entropy four-current obtained using Grad's method, there is a non-vanishing entropy flux in the present third-order expression. We further quantify the effect of the higher-order entropy density in the case of boost-invariant onedimensional longitudinal expansion of a system. We demonstrate that the results obtained using third-order evolution equation for shear stress tensor, derived by employing the method of Chapman-Enskog expansion, show better agreement with the exact solution of the Boltzmann equation as well as with the parton cascade BAMPS, as compared to those obtained using the third-order equations from the method of Grad's 14-moment approximation.

Physical Review Letters

We present the first comparisons of experimental data with phenomenological results from 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP which naturally includes both shear and bulk viscous effects. The 3+1d aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of THERMINATOR 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature TFO = 130 MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Physical Review C

We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boostinvariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4πη/s ∼ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear viscosity to entropy density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4πη/s in Israel-Stewart viscous hydrodynamics whereas in anisotropic hydrodynamics it has a maximum at 4πη/s ∼ 10. For all 4πη/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.

Physical Review C

We study dynamic features of a plasma consisting of gluons whose infrared dynamics is improved by the Gribov-Zwanziger quantization. This approach embodies essential features of color confinement which set the plasma apart from conventional quasiparticle systems in several aspects. Our study focusses on a boost-invariant expansion for in-and out-of-equilibrium settings within the relaxation time approximation, which at late times can be characterized by the sound velocity, cs, and the shear, η, and bulk, ζ, viscosities. We obtain explicit expressions for the transport coefficients η and ζ and check that they are consistent with the numerical solutions of the kinetic equation. At high temperature, keeping both the Gribov parameter and the relaxation time constant, we find a scaling ζ/η ∝ 1 /3 − c 2 s which manifests strong breaking of conformal symmetry in contrast to the case of weakly coupled plasmas.

Journal of Physics: Conference Series

Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory.

Journal of Physics: Conference Series

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Physical Review D

We compute dilepton production from the deconfined phase of the quark-gluon plasma using leading-order (3+1)-dimensional anisotropic hydrodynamics. The anisotropic hydrodynamics equations 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 final results, we present predictions for high-energy dilepton yields as a function of invariant mass, transverse momentum, and pair rapidity. We demonstrate that highenergy dilepton production is extremely sensitive to the assumed level of initial momentum-space anisotropy of the quark-gluon plasma. As a result, it may be possible to experimentally constrain the early-time momentum-space anisotropy of the quark-gluon plasma generated in relativistic heavy ion collisions using high-energy dilepton yields.

Physical Review C

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 anisotropic hydrodynamics, which treats the large initial pressure anisotropy in a non-perturbative fashion. The results obtained with second-order viscous hydrodynamics depend on the particular choice of the second-order terms included, which suggests that the latter should be included in the most complete way. The results of anisotropic hydrodynamics and viscous hydrodynamics agree for the central hot part of the system, however, they differ at the edges where the approach of anisotropic hydrodynamics helps to control the undesirable growth of viscous corrections observed in standard frameworks.

Physical Review C

We compare phenomenological results from 3+1d quasiparticle anisotropic hydrodynamics (aHy-droQP) with experimental data collected in LHC 2.76 TeV Pb-Pb collisions. In particular, we present comparisons of particle spectra, average transverse momentum, elliptic flow, and HBT radii. The aHydroQP model relies on the introduction of a single temperature-dependent quasiparticle mass which is fit to lattice QCD data. By taking moments of the resulting Boltzmann equation, we obtain the dynamical equations used in the hydrodynamic stage which include the effects of both shear and bulk viscosities. At freeze-out, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface to convert to hadrons. To model the production and decays of the hadrons we use THERMINATOR 2 which is customized to sample from ellipsoidal momentum-space distribution functions. Using smooth Glauber initial conditions, we find very good agreement with many heavy-ion collision observables.

Physical Review C

Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry. Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems.

Physical Review C

Anisotropic-hydrodynamics framework is used to describe a mixture of quark and gluon fluids. The effects of quantum statistics, finite quark mass, and finite baryon number density are taken into account. The results of anisotropic hydrodynamics are compared with exact solutions of the coupled kinetic equations for quarks and gluons in the relaxation time approximation. The overall very good agreement between the hydrodynamic and kinetic-theory results is found.

Journal of Physics G: Nuclear and Particle Physics

Detailed study of thermalization of the momentum spectra of partons produced via decays of the color flux tubes due to the Schwinger tunneling mechanism is presented. The collisions between particles are included in the relaxation time approximation specified by different values of the shear viscosity to entropy density ratio. At first we show that, to a good approximation, the transverse-momentum spectra of the produced patrons are exponential, irrespectively from the assumed value of the viscosity of the system and the freeze-out time. This thermal-like behaviour may be attributed to specific properties of the Schwinger tunneling process. In the next step, in order to check the approach of the system towards genuine local equilibrium, we compare the local slope of the model transverse-momentum spectra with the local slope of the fully equilibrated reference spectra characterised by the effective temperature that reproduces the energy density of the system. We find that the viscosity corresponding to the AdS/CFT lower bound is necessary for thermalization of the system within about two fermis.

Physical Review D

Exact correspondence between Israel-Stewart theory and first-order causal and stable hydrodynamics is established for the boost-invariant massive case with zero baryon density and the same constant relaxation times used in the shear and bulk sectors. Explicit expressions for the temperature dependent regulators are given for the case of a relativistic massive gas. The stability and causality conditions known in the first-order approach are applied and one finds that one of them is violated in this case.

Physical Review D

Using the classical description of spin degrees of freedom, we extend recent formulation of the perfectfluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic equations for massive particles with spin 1=2, with the collision terms treated in the relaxation time approximation. The kinetic-theory framework determines the structure of viscous and diffusive terms and allows to explicitly calculate a complete set of new kinetic coefficients that characterize dissipative spin dynamics.

Journal of High Energy Physics, 2021

We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.

Physical Review C, 2012

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 oneparticle 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 numerical implementations: one which is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions; and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the lab-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity to entropy ratio, proper time, and impact parameter.

Physical Review D, 2014

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3) q ⊗ SO(1, 1) ⊗ Z 2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

Physical Review C, 2015

We generalize the derivation of viscous anisotropic hydrodynamics from kinetic theory to allow for non-zero particle masses. The macroscopic theory is obtained by taking moments of the Boltzmann equation after expanding the distribution function around a spheroidally deformed local momentum distribution whose form has been generalized by the addition of a scalar field that accounts nonperturbatively (i.e. already at leading order) for bulk viscous effects. Hydrodynamic equations for the parameters of the leading-order distribution function and for the residual (next-to-leading order) dissipative flows are obtained from the three lowest moments of the Boltzmann equation. The approach is tested for a system undergoing (0+1)-dimensional boost-invariant expansion for which the exact solution of the Boltzmann equation in relaxation time approximation is known. Nonconformal viscous anisotropic hydrodynamics is shown to approximate this exact solution more accurately than any other known hydrodynamic approximation.

Physical Review D

Physical Review D

Advances in High Energy Physics, 2013

We review the various aspects of anisotropic quark-gluon plasma (AQGP) that have recently been discussed by a number of authors. In particular, we focus on the electromagnetic probes of AQGP, inter quark potential, quarkonium states in AQGP, and the nuclear modifications factor of various bottomonium states using this potential. In this context, we will also discuss the radiative energy loss of partons and nuclear modification factor of light hadrons in the context of AQGP. The features of the wake potential and charge density due to the passage of jet in AQGP will also be demonstrated.

Physical Review C, 2012

We calculate the gluon dissociation cross-section in an anisotropic quark gluon plasma expected to be formed in relativistic nucleus-nucleus collisions. It is shown that the thermally weighted cross-section of gluon dissociation undergoes modification in anisotropic plasma affecting the J/ψ survival probability. The dependence of the cross section on the direction of propagation of the charmonium with respect to the anisotropy axis is presented. Survival probability of J/ψ in two different space time models of anisotropic quark gluon plasma (AQGP) has been calculated. It is shown that depending upon the initial conditions (corresponding to RHIC energies), the survival probability in AQGP differs from that in isotropic QGP both in the central as well as forward rapidity regions. For initial conditions relevant for LHC energies, marginal difference between the the two space time models has been observed with a given initial conditions.

Journal of High Energy Physics, 2014

We present a type IIB supergravity solution dual to a spatially anisotropic N = 4 super Yang-Mills plasma at finite U(1) chemical potential and finite temperature. The effective five-dimensional gravitational theory is a consistent Einstein-Maxwell-dilaton-Axion truncation of the gauged supergravity. We obtain the solutions both numerically and analytically. We study the phase structure and thermodynamic instabilities of the solution, and find new instabilities independent of the renormalization scheme.

Physical Review D, 2018

Journal of High Energy Physics, 2017

The pre-equilibrium evolution of a quark-gluon plasma produced in a heavy-ion collision is studied in the framework of kinetic theory. We discuss the approach to local thermal equilibrium, and the onset of hydrodynamics, in terms of a particular set of moments of the distribution function. These moments quantify the momentum anisotropies to a finer degree than the commonly used ratio of longitudinal to transverse pressures. They are found to be in direct correspondence with viscous corrections of hydrodynamics, and provide therefore an alternative measure of these corrections in terms of the distortion of the momentum distribution. As an application, we study the evolution of these moments by solving the Boltzmann equation for a boost invariant expanding system, first analytically in the relaxation time approximation, and then numerically for a quark-gluon plasma with a collision kernel given by leading order 2 ↔ 2 QCD matrix elements in the small angle approximation.

The European Physical Journal C

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 results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function ($$q \rightarrow 1$$ q → 1 ). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for ev...

Advances in High Energy Physics, 2016

Relativistic hydrodynamics has been quite successful in explaining the collective behaviour of the QCD matter produced in high energy heavy-ion collisions at RHIC and LHC. We briefly review the latest developments in the hydrodynamical modeling of relativistic heavy-ion collisions. Essential ingredients of the model such as the hydrodynamic evolution equations, dissipation, initial conditions, equation of state, and freeze-out process are reviewed. We discuss observable quantities such as particle spectra and anisotropic flow and effect of viscosity on these observables. Recent developments such as event-by-event fluctuations, flow in small systems (proton-proton and proton-nucleus collisions), flow in ultracentral collisions, longitudinal fluctuations, and correlations and flow in intense magnetic field are also discussed.

Physical review, 2013

We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggested by the Entropy Production Principle; the evolution equation is obtained by the method of moments, and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmann's equation in 0+1 dimensions and show that it tracks kinetic theory better than second order fluid dynamics.

Physical review, 2012

Starting from kinetic theory, we obtain a nonlinear dissipative formalism describing the nonequilibrium evolution of scalar colored particles coupled selfconsistently to nonabelian classical gauge fields. The link between the one-particle distribution function of the kinetic description and the variables of the effective theory is determined by extremizing the entropy production. This method does not rely on the usual gradient expansion in fluid dynamic variables, and therefore the resulting effective theory can handle situations where these gradients (and hence the momentum-space anisotropies) are expected to be large. The formalism presented here, being computationally less demanding than kinetic theory, may be useful as a simplified model of the dynamics of color fields during the early stages of heavy ion collisions and in phenomena related to parton energy loss.

Physical Review D

We formulate the first-order dissipative anisotropic hydrodynamical theory for a relativistic conformal uncharged fluid, which generalizes the Bemfica-Disconzi-Noronha-Kovtun first-order viscous fluid framework. Our approach maintains causal behavior in the nonlinear regime with or without general relativity coupling, and we derive and analyze the constraints on transport coefficients imposed by causality. We demonstrate the causal and stable behavior of our theory in specific cases, including the discussion of nonlinear causality as well as stability for linearized perturbations. We apply our newly developed first-order anisotropic theory to the Bjorken flow and show how causality and stability impose constraints on the behavior of the early-time attractor.