Substantial collective flow is observed in collisions between large nuclei at high energy, as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well-reproduced by perfect fluid dynamics. In a separate development, calculation of the dimensionless ratio of shear viscosity eta to entropy density s by Kovtun, Son and Starinets within AdS/CFT yields eta/s = 1/4pi, and they conjectured that this is a lower bound for any physical system. It is shown that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio eta/s. Therefore it is possible that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD via the viscosity to entropy ratio in addition to and independently of the equation of state.
Substantial collective flow is observed in collisions between large nuclei at RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well-reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity $η$ to entropy density $s$ by Kovtun, Son and Starinets within anti-de Sitter space/conformal field theory yields $η/s = \hbar/4πk_B$ which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show…
We show that first approximations to the bulk viscosity $η_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of $η_v$ on the factor $(\frac 13 - v_s^2)$ is demonstrated in the Chapman-Enskog approximation as well as the variational and relaxation time approaches. The interesting feature of bulk viscosity is that the dominant contributions at a given temperature arise from particles which are neither extremely nonrelativistic nor extremely relativistic. Numerical results f…
Longitudinal hydrodynamic expansion of the fluid created in relativistic heavy-collisions is considered taking into account shear viscosity. Both a on-vanishing viscosity and a soft equation of state make particle distributions in rapidity narrower. The presence of viscosity has dramatic consequence on the value of the initial energy density. The reduction of the longitudinal work and dissipative processes due to the shear viscosity, increase the total entropy and the particle multiplicity at central rapidities. The total energy in the collision, dominated by the longitudinal motion, is conser…
This paper presents how thermal mean field effects are incorporated consistently in the hydrodynamical modelling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered i…
We discuss the influence of different initial conditions for the stress tensor and the effect of bulk viscosity on the expansion and cooling of the fireball created in relativistic heavy-ion collisions. In particular, we explore the evolution of longitudinal and transverse components of the pressure and the extent of dissipative entropy production in the one-dimensional, boost-invariant hydrodynamic model. We find that a bulk viscosity consistent with recent estimates from lattice QCD further slows the equilibration of the system, however it does not significantly increase the entropy produced…
We study the effects of the shear and bulk viscosities in the hadronic phase on the expansion of the fireball and on the particle production in relativistic heavy ion collisions. Comparing simulation with or without viscosity in the hadronic matter we find that elliptic flow observables strongly dependent on dissipative effects in the late stage. On the other hand, interferometry radii are sensitive, through the early transverse flow, on the value of the viscosity at high temperatures. We present first calculations including the effects of bulk viscosity in the hadronic phase and in the hadron…
We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter $z=e^{βμ}$, which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theoretic framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides a possible zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an addition…
The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of \emph{non-relativistic} quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $ζ(ω)$ and $η(ω)$ respectively, to derive exact, non-perturbative results. Our results include: a microscopic connection between the shear viscosity $η$ and the normal fluid density $ρ_n$; sum rules for $ζ(ω)$ and $η(ω)$ and their evolution through the BCS-BEC crossove…
We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation Theory at low and moderate temperatures, below any phase transition to a quark-gluon plasma phase. We argue that inelastic processes are irrelevant and exponentially suppressed at low temperatures. Since the system falls out of chemical equilibrium upon expansion,a pion chemical potential must be introduced, so we extend the existing theory to include it. We control the zero modes of the collision operator and Landau's conditions of fit when solving the Boltzmann equation with the elastic collision kernel. The dependen…
We give an review the HBT puzzle, and argue that its resolution requires the introduction of new physics close to the phase transition scale. We argue that a candidate for this new physics is bulk viscosity, recently postulated to peak, and even diverge, close to the phase transition temperature. We show that such a viscosity peak can force the system created in heavy ion collisions to become unstable, and filament into fragments whose size is weakly dependent on the global size of the system, thereby triggering freeze-out.
We compute the shear viscosity of a two dimensional Fermi gas interacting via a short range potential with scattering length $a_{2d}$ in kinetic theory. We find that kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two dimensional gas is comparable to that of the three dimensional unitary gas. We use our results to compute the damping of collective modes in a trapped Fermi gas, and compare to experimental data recently obtained in E. Vogt et al., arXiv:1111.1173.
The shear viscosity $η$ has been calculated by using the Green-Kubo relation in the framework of a partonic transport approach solved at cascade level. We compare the numerical results for $η$ obtained from the Green-Kubo correlator with the analytical formulas in both the Relaxation Time Approximation (RTA) and the Chapman-Enskog approximation (CE). We investigate and emphasize the differences between the isotropic and anisotropic cross sections and between the massless and massive particles. We show that in the range of temperature explored in a Heavy Ion collision and for pQCD-like cross se…
We show how the measurement of appropriately constructed particle-energy/momentum correlations allows access to the bulk viscosity of strongly interacting hadron matter in heavy ion collisions. This measurement can be performed by the LHC and RHIC experiments in events with high-particle multiplicity, following up on existing estimates of the shear viscosity based on elliptic flow.
We review the properties of the strongly interacting quark-gluon plasma (QGP) at finite temperature $T$ and baryon chemical potential $μ_B$ as created in heavy-ion collisions at ultrarelativistic energies. The description of the strongly interacting (non-perturbative) QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature $T_C$ from lattice QCD. Based on a microscopic transport description of heavy-ion collisions we discuss …
The shear viscosity, eta, of a fermi gas with non-relativistic conformal symmetry in two spatial dimensions is investigated. We find that eta/s, s being the entropy density, diverges as a gas of free particles in this system. It is in contrast to the eta/s=1/(4 pi) found using non-relativistic AdS/CFT correspondence, which requires a strongly interacting CFT. It implies the unitary fermi gas in two spatial dimensions is not likely to have a weakly interacting gravity dual.
A 1+3 dimensional solution of relativistic hydrodynamics is analyzed in this paper. Momentum distribution and other observables are calculated from the solution and compared to hadronic measurements from the Relativistic Heavy Ion Collider (RHIC). The solution is compatible with the data, but only the freeze-out point of the evolution is determined. Many equation of states and initial states (initial temperatures) are valid with the same freeze-out distribution, thus the same hadronic observables. The observable that would distinguish between these initial temperatures is momentum distribution…
Substantial collective flow is observed in collisions between large nuclei at high energy, and the data are well-reproduced by perfect fluid dynamics. In a separate development, calculation of the dimensionless ratio of shear viscosity $η$ to entropy density within AdS/CFT yields $η/s = 1/4π$, which has been conjectured to be a lower bound for any physical system. It is shown that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio $η/s$. Conversely, there are indications that the ratio of bulk vi…
Collective flow, its anisotropies and its event-to-event fluctuations in relativistic heavy-ion collisions, and the extraction of the specific shear viscosity of quark-gluon plasma (QGP) from collective flow data collected in heavy-ion collision experiments at RHIC and LHC are reviewed. Specific emphasis is placed on the similarities between the Big Bang of our universe and the Little Bangs created in heavy-ion collisions.
Shear viscosity $η$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number densi…
We study the viscosity and thermodynamic properties of QGP at RHIC by employing the recently extracted equilibrium distribution functions from two hot QCD equations of state of $O(g^5)$ and $O(g^6\ln(1/g))$ respectively. After obtaining the temperature dependence of energy density, and entropy density, we focus our attention on the determination of shear viscosity for a rapidly expanding interacting plasma, as a function of temperature. We find that interactions significantly decrease the shear viscosity. They decrease the viscosity to entropy density ratio, $η/{\mathcal S}$ as well.
Posterior distributions for physical parameters describing relativistic heavy-ion collisions, such as the viscosity of the quark-gluon plasma, are extracted through a comparison of hydrodynamic-based transport models to experimental results from 100$A$ GeV + 100$A$ GeV Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). By simultaneously varying six parameters and by evaluating several classes of observables, we are able to explore the complex intertwined dependencies of observables to model parameters. We obtain a full multi-dimensional posterior distribution for the model output …
We investigate the consequences of a nonzero bulk viscosity coefficient on the transverse momentum spectra, azimuthal momentum anisotropy, and multiplicity of charged hadrons produced in heavy ion collisions at LHC energies. The agreement between a realistic 3D hybrid simulation and the experimentally measured data considerably improves with the addition of a bulk viscosity coefficient for strongly interacting matter. This paves the way for an eventual quantitative determination of several QCD transport coefficients from the experimental heavy ion and hadron-nucleus collision programs.
The expansion of the fireball created in relativistic heavy ion collisions is described using the 3+1D hydrodynamical model. Experimentally observed transverse momentum spectra at different rapdities, elliptic flow and HBT correlations of produced particles can be reproduced. We give estimates of shear viscosity corrections at freeze-out, which we find important only for the elliptic flow coefficient.
Photons and dileptons are being used to probe the properties of nuclear and quark-gluon matter at high energy densities. This is an area where theory and experiment are driving each other to obtain solid results. However, it is important to clearly separate the assumptions and conclusions concerning the correlation and response functions of a system in thermal equilibrium from the space-time dynamics used to model the evolution of the matter created in the nuclear collision.
New, analytic solutions of relativistic viscous hydrodynamics are presented, describing expanding fireballs with Hubble-like velocity profile and ellipsoidal symmetry, similar to fireballs created in heavy ion collisions. We find that with these specifications, one obtains solutions where the shear viscosity essentially does not influence the time evolution of the system, thus these solutions are particularly adept tools to study the effect of bulk viscosity alone, which always results in a slower decrease of energy density as well as temperature compared to the case of perfect fluid. We inves…
The ratio eta/s, shear viscosity (eta) to entropy density (s), reaches its local minimum at the (second order) phase transition temperature in a wide class of systems. It was suspected that this behavior might be universal. However, a counterexample is found in a system of two weakly self-interacting real scalar fields with one of them condensing at low temperatures while the other remains in the symmetric phase. There is no interaction between the two fields. The resulting eta/s is monotonically decreasing in temperature despite the phase transition.
The collective behavior of hadrons and of electromagnetic radiation in heavy-ion collisions has been widely used to study the properties of the the Quark-Gluon Plasma (QGP). Indeed this collectivity, as measured by anisotropic flow coefficients, can be used to constrain the transport properties of QGP. The goal of this contribution is to investigate the influence of the specific bulk viscosity ($ζ/s$) on dilepton production, both at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. We explore the sensitivity of dileptons to dynamical features that bulk viscosity …
Thermodynamic and transport properties of nuclear fireball created in the central region of heavy-ion collisions below 400 MeV/nucleon are investigated within the isospin-dependent quantum molecular dynamic (IQMD) model. These properties including the density, temperature, chemical potential, entropy density ($s$) and shear viscosity ($η$), are calculated by a generalized hot Thomas Fermi formulism and a parameterized function, which was developed by Danielewicz. As the collision goes on, a transient minimal $η/s=5/4π-10/4π$ occurs in the largest compression stage. Besides, the relationship of…
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1 with a temperature dependent specific shear viscosity (eta/s)(T), we present a detailed study of the influence of a large hadronic shear viscosity and its corresponding relaxation time tau_pi on the transverse momentum spectra and elliptic flow of hadrons produced in 200 A GeV Au+Au collisions. Although theory, in principle, predicts a well-defined relation T*tau_pi = kappa(T)*(eta/s)(T), the precise form of kappa(T) for the matter created in relativistic heavy-ion collisions is not known. For the popular choice kappa=3 the hadron s…
We have attempted to build first some simplified model to map the interaction of quarks and gluons, which can be contained by their thermodynamical quantity like entropy density, obtained from calculation of lattice quantum chromo dynamics (LQCD). With respect to entropy density of the standard non-interacting massless quark gluon plasma (QGP), its interacting values from LQCD simulation are reduced as we go from higher to lower temperature through the cross-over of quark-hadron phase transition. By parameterizing increasing degeneracy factor or increasing interaction-fugacity or decreasing th…
I derive an exact integral expression for the ratio of shear viscosity over entropy density $\fracη{s}$ for the massless (critical) O(N) model at large N with quartic interactions. The calculation is set up and performed entirely from the field theory side using a non-perturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, $\fracη{s}$ is evaluated numerically at all values of the coupling. For infinite coupling, I find $\fracη{s}\simeq 0.42(1)\times N$. I show that this strong coupling result for the viscosity is universal for a large class of inte…
Recent estimates for the electromagnetic fields produced in the early stages of non-central ultra-relativistic heavy ion collisions indicate the presence of magnetic fields $B\sim \mathcal{O}(0.1-15\,m_π^2)$, where $m_π$ is the pion mass. It is then of special interest to study the effects of strong (Abelian) magnetic fields on the transport coefficients of strongly coupled non-Abelian plasmas, such as the quark-gluon plasma formed in heavy ion collisions. In this work we study the anisotropy in the shear viscosity induced by an external magnetic field in a strongly coupled $\mathcal{N} = 4$ S…
We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system. Dissipative hydrodynamic equations and the form of transport coefficients is subsequently derived for this case. We find that the shear and bulk viscosity coefficients, as well as the baryon charge conductivity are independent of the transiti…
We numerically simulate gravitational shock wave collisions in a holographic model dual to a non-conformal four-dimensional gauge theory. We find two novel effects associated to the non-zero bulk viscosity of the resulting plasma. First, the hydrodynamization time increases. Second, if the bulk viscosity is large enough then the plasma becomes well described by hydrodynamics before the energy density and the average pressure begin to obey the equilibrium equation of state. We discuss implications for the quark-gluon plasma created in heavy ion collision experiments.
The coefficients of diffusion, thermal conductivity, and shear viscosity are calculated for a system of non-relativistic particles interacting via a delta-shell potential V(r)=-v δ(r-R) when the average distance between particles is smaller than R. The roles of resonances and long scattering lengths including the unitary limit are examined. Results for ratios of diffusion to viscosity and viscosity to entropy density are presented for varying scattering lengths.
We investigate general frameworks for calculating transport coefficients for quasiparticle theories at finite temperature. Hadronic transport coefficients are then computed using the linear sigma model (LSM). The bulk viscosity over entropy density ($ζ/s$) is evaluated in the relaxation time approximation (RTA) and the specific shear viscosity ($η/s$) and static electrical conductivity ($σ_{el}/T$) are both obtained in the RTA and using a functional variational approach. Results are shown for different values of the scalar-isoscalar hadron vacuum mass with in-medium masses for the interacting …
We review the transport properties of the strongly interacting quark-gluon plasma (QGP) created in heavy-ion collisions at ultrarelativistic energies, i.e. out-of equilibrium, and compare them to the equilibrium properties. The description of the strongly interacting (non-perturbative) QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. We study the transport coefficients such as the ratio of shear…
In order to study the temperature dependence of the quark-hadron phase structure and the QCD equation of state in vanishing and finite magnetic field, the SU(3) Polyakov linear-sigma model is utilized. In mean field approximation, the dependence of various magnetic properties such as magnetization, magnetic susceptibility and magnetic catalysis is analyzed in finite magnetic field. Furthermore, the influences of finite magnetic field on the temperature dependence of some transport properties (viscosity and conductivity) from Green-Kubo correlation are characterized.
