Effects of viscosity and thermal conductivity on the dynamics of first-order phase transitions are studied. The nuclear gas-liquid and hadron-quark transitions in heavy-ion collisions are considered. We demonstrate that at non-zero thermal conductivity, $κ\neq 0$, onset of spinodal instabilities occurs on an isothermal spinodal line, whereas for $κ=0$ instabilities take place at lower temperatures, on an adiabatic spinodal.
The two-point correlation functions of kaonic viscous stress tensors and electro-magnetic currents have been calculated respectively to estimate the contributions of the strange sector in the shear viscosity and electrical conductivity of hadronic medium. In the one-loop correlators, kaon propagators contain a non-zero thermal width that leads to non-divergent values of transport coefficients. With the help of effective Lagrangian densities of strange hadrons, we have calculated in-medium self-energy of kaon for different possible mesonic loops, whose imaginary part provide the estimation of k…
We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic medium, which goes from without to with magnetic field picture and then their simplified massless expressions. In presence of magnetic field, 5 independent velocity gradient tensors can be designed, so their corresponding proportional coefficients, connected with the viscous stress tensor provide us 5 shear viscosity coefficients. In existing litterateurs, two sets of tensors are available. Starting from them, present work has obtained two sets of expressions for 5 shear viscosity coefficien…
The temperature and density dependence of the relaxation times, thermal conductivity, shear viscosity and bulk viscosity for a hot and dense gas consisting of pions, kaons and nucleons have been evaluated in the kinetic theory approach. The in-medium cross-sections for $ππ$, $πK$ and $πN$ scatterings were obtained by using complete propagators for the exchanged $ρ$, $σ$, $K^*$ and $Δ$ excitations derived using thermal field theoretic techniques. Notable deviations can be observed in the temperature dependence of $η$, $ζ$ and $λ$ when compared with corresponding calculations using vacuum cross-…
A novel higher order theory of relaxation of heat and viscosity is proposed based on corrections to the traditional treatment of the relativistic energy density. In the framework of generalized Bjorken scaling solution to accelerating longitudinal flow we point out that the energy flux can be consequently set to zero in the stationary case, independently of the choice of a specific local rest frame, like the Landau-Lifshitz or Eckart one. We investigate and compare several cooling and re-heating scenarios for the Quark Gluon Plasma (QGP) within this approach.
The transport coefficients of strongly interacting matter are currently subject of intense theoretical and phenomenological studies due to their relevance for the characterization of the quark-gluon plasma produced in ultra relativistic heavy-ion collisions (uRHIC). We discuss the connection between the shear viscosity to entropy density ratio, $η/s$, and the electric conductivity, $σ_{el}$. Once the relaxation time is tuned to have a minimum value of $η/s=1/4π$ near the critical temperature $T_c$, one simultaneously predicts $σ_{el}/T$ very close to recent lQCD data. More generally, we discus…
We calculate two transport coefficients -- the shear viscosity over entropy ratio $η/s$ and the ratio of the electric conductivity to the temperature $σ_0/T$ -- of strongly interacting quark matter within the extended $N_f=3$ Polyakov Nambu-Jona-Lasinio (PNJL) model along the crossover transition line for moderate values of baryon chemical potential $0 \leq μ_B \leq 0.9$ GeV as well as in the vicinity of the critical endpoint (CEP) and at large baryon chemical potential $μ_B=1.2$ GeV, where the first-order phase transition takes place. The evaluation of the transport coefficients is performed …
We calculate the shear viscosity $η$ and thermal conductivity $κ$ of a nuclear pasta phase in neutron star crusts. This involves complex non-spherical shapes. We use semiclassical molecular dynamics simulations involving 40,000 to 100,000 nucleons. The viscosity $η$ can be simply expressed in terms of the height $Z^*$ and width $Δq$ of the peak in the static structure factor $S_p(q)$. We find that $η$ increases somewhat, compared to a lower density phase involving spherical nuclei, because $Z^*$ decreases from form factor and ion screening effects. However, we do not find a dramatic increase i…
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 calculation of the transport coefficients of the strong quark-gluon plasma (sQGP), i.e. sheer viscosity $η$, heat conductivity $\gk$ and bulk viscosity $ζ$, in the first Chapman-Enskog approximation is presented. Their formulation in terms of two-fold integrals depending on the particle interaction, known as relativistic omega integrals, is derived and their evaluation in the ultrarelativistic limit is worked out assuming a cross section independent of the relative and total momentum of two colliding particles. We find a suppression of the bulk viscosity and a pronounced temperature depend…
We study the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$, different shear relaxation times $τ_π$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear …
We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and independent of the total system volume. These clusters maintain the pre-existing outward-going flow…
We propose a method for extracting the shear viscosity over entropy density ratio (eta/s) of the quark-gluon plasma from experimental data. We argue that uncertainty due to poor knowledge of the earliest stages of a heavy-ion collision is smallest for ultra-central events. The most precise value of eta/s can thus be obtained from a global fit to p_T-integrated Fourier harmonics of azimuthal correlations. We further outline a method for quantifying the overall uncertainty in the extracted value. Only after a comprehensive and systematic accounting of all sources of uncertainty can a reliable me…
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.
We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio eta/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.
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.
We compute the thermal conductivity and sound attenuation length of a dilute atomic Fermi gas in the framework of kinetic theory. Above the critical temperature for superfluidity, T_c, the quasi-particles are fermions, whereas below T_c, the dominant excitations are phonons. We calculate the thermal conductivity in both cases. We find that at unitarity the thermal conductivity κin the normal phase scales as κ~ T^{3/2}. In the superfluid phase we find κ~ T^{2}. At high temperature the Prandtl number, the ratio of the momentum and thermal diffusion constants, is 2/3. The ratio increases as the t…
The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are …
We compute the shear viscosity and the electrical conductivity in gauge theories with massive fermions at leading order in the large N_f expansion. The calculation is organized using the 1/N_f expansion of the 2PI effective action to next-to-leading order. We show explicitly that the calculation is gauge fixing independent and consistent with the Ward identity. We find that these transport coefficients depend in a nontrivial manner on the coupling constant and fermion mass. For large mass, both the shear viscosity and the electrical conductivity go to zero.
Finite size consideration of matter significantly affects transport coefficients like shear viscosity, bulk viscosity, electrical conductivity, which we have investigated here in the framework of the Polyakov-Nambu-Jona-Lasinio model. Owing to the basic quantum mechanics, a non-zero lower momentum cut-off is implemented in momentum integrations, used in the expressions of constituent quark masses and transport coefficients. When the system size decreases, the values of these trans- port coefficients are enhanced in low temperature range. At high temperature domain, shear viscos- ity and electr…
Shear viscosity and electrical conductivity of rotating quark matter in Nambu--Jona-Lasinio Model
Indian Institute of Technology Bhilai（印度理工学院比莱分校）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Joint Institute for Nuclear Research（苏联联合核子研究所）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
We study the effects of bulk viscosity on pT spectra and elliptic flow in heavy ion collisions. For this purpose we compute the dissipative correction df to the single particle distribution functions in leading-log QCD, and in several simplified models. We consider, in particular, the relaxation time approximation and a kinetic model for the hadron resonance gas. We implement these distribution functions in a hydrodynamic simulation of Au + Au collisions at RHIC. We find significant corrections due to bulk viscosity in hadron pT spectra and the differential elliptic flow parameter v2(pT). Thes…
Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($σ_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamic…
A temperature dependent bulk viscosity coefficient is used in 3+1D hydrodynamic simulations. I study the effect of the increase of bulk viscosity around the critical temperature on the system dynamics in central Pb+Pb collisions at $\sqrt{s_{NN}}=2760$~GeV. With increasing bulk viscosity the life-time of the system increases slightly. Also the shape of the freeze-out hypersurface changes, the outer layers of the fireball live longer. This effect causes a small reduction of the ratio of two interferometry radii $R_{out}/R_{side}$, improving the agreement with experimental data.
The correlation between the elliptic flow $v_2$ scaled by the impact parameter $b$ and the shear viscosity $η$ as well as the specific viscosity $η/s$, defined as the ratio of the shear viscosity to the entropy density $s$, is investigated for the first time in intermediate-energy heavy-ion collisions based on an isospin-dependent quantum molecular dynamic model. The elliptic flow is calculated at balance energies to exclude the geometric influence such as the blocking effect from the spectators. Our study shows that $v_{2}/b$ decreases almost linearly with increasing $η$, consistent with that…
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.
The effect of a temperature dependent bulk viscosity to entropy density ratio~($ζ/s$) along with a constant shear viscosity to entropy density ratio~($η/s$) on the space time evolution of the fluid produced in high energy heavy ion collisions have been studied in a relativistic viscous hydrodynamics model. The boost invariant Israel-Stewart theory of causal relativistic viscous hydrodynamics is used to simulate the evolution of the fluid in 2 spatial and 1 temporal dimension. The dissipative correction to the freezeout distribution for bulk viscosity is calculated using Grad's fourteen moment …
Starting from IP-Glasma initial conditions, we investigate the effects of bulk pressure on thermal dilepton production at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) energies. Though results of the thermal dilepton $v_2$ under the influence of both bulk and shear viscosity is presented for top RHIC energy, more emphasis is put on LHC energy where such a calculation is computed for the first time. The effects of the bulk pressure on thermal dilepton $v_2$ at the LHC are explored through bulk-induced modifications on the dilepton yield.
We describe ultra-relativistic heavy ion collisions at RHIC and the LHC with a hybrid model using the IP-Glasma model for the earliest stage and viscous hydrodynamics and microscopic transport for the later stages of the collision. We demonstrate that within this framework the bulk viscosity of the plasma plays an important role in describing the experimentally observed radial flow and azimuthal anisotropy simultaneously. We further investigate the dependence of observables on the temperature below which we employ the microscopic transport description.
Shear Viscosity and Electrical Conductivity of Rotating Nuclear Medium in Hadron Resonance Gas and Nambu-Jona Lasinio Models
Indian Institute of Technology Bhilai（印度理工学院比莱分校）；National Institute of Technology Durgapur（杜尔加布尔国家技术学院）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Joint Institute for Nuclear Research（联合核子研究所）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We …
We perform viscous hydrodynamic calculations in 2+1 dimensions to investigate the influence of bulk viscosity on the viscous suppression of elliptic flow in non-central heavy-ion collisions at RHIC energies. Bulk and shear viscous effects on the evolution of radial and elliptic flow are studied with different model assumptions for the transport coefficients. We find that the temperature dependence of the relaxation time for the bulk viscous pressure, especially its critical slowing down near the quark-hadron phase transition at T_c, partially offsets effects from the strong growth of the bulk …
We study entropy production in the early stage of high-energy heavy-ion collisions due to shear viscosity. We employ the second-order theory of Israel-Stewart with two different stress relaxation times, as appropriate for strong coupling or for a Boltzmann gas, respectively, and compare the hydrodynamic evolution. Based on present knowledge of initial particle production, we argue that entropy production is tightly constrained. We derive new limits on the shear viscosity to entropy density ratio $η/s$, independent from elliptic flow effects, and determine the corresponding Reynolds number. Fur…
In recent years, there has been a significant effort to extract the temperature-dependent shear ($η/s$) and bulk ($ζ/s$) viscosity over entropy ratios of the quark-gluon plasma from a global comparison of heavy-ion data with results of hydrodynamic simulations. However, anisotropic flow, which is arguably the most sensitive probe of viscosity, is only sensitive to an {\it effective\/} viscosity over entropy ratio, which is obtained by taking a weighted average over the temperature, and summing the contributions of shear and bulk. We estimate this effective viscosity using existing first-princi…
The shear viscosity of the crust might have a damping effect on the amplitude of r-modes of rotating neutron stars. This damping has implications for the emission of gravitational waves. We calculate the contribution to the shear viscosity coming from the ions using both semi-analytical methods, that consider binary collisions, and Molecular Dynamics simulations. We compare these results with the contribution coming from electrons. We study how the shear viscosity depends on density for conditions of interest in neutron star envelopes and outer crusts. In the low density limit, we find good ag…
Relativistic heavy ion collisions generate nuclear-sized droplets of quark-gluon plasma (QGP) that exhibit nearly inviscid hydrodynamic expansion. Smaller collision systems such as p+Au, d+Au, and $^{3}$He+Au at the Relativistic Heavy Ion Collider, as well as p+Pb and high-multiplicity p+p at the Large Hadron Collider may create even smaller droplets of QGP. If so, the standard time evolution paradigm of heavy ion collisions may be extended to these smaller systems. These small systems present a unique opportunity to examine pre-hydrodynamic physics and extract properties of the QGP, such as t…
We show that in asymmetric heavy-ion collisions, especially off-central Cu+Au collisions, a sizable strength of electric field directed from Au nucleus to Cu nucleus is generated in the overlapping region, because of the difference in the number of electric charges between the two nuclei. This electric field would induce an electric current in the matter created after the collision, which result in a dipole deformation of the charge distribution. The directed flow parameters $v_1^{\pm}$ of charged particles turn out to be sensitive to the charge dipole and provide us with information about ele…
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…
Recent work has shown that a temperature dependence of the shear viscosity to entropy ratio, $η/s$, influences the collective flow pattern in heavy-ion collisions in characteristic ways that can be measured by studying hadron transverse momentum spectra and their anisotropies. Here we point out that it also affects the pair momentum dependence of the Hanbury-Brown$-$Twiss (HBT) radii (the source size parameters extracted from two-particle intensity interferometry) and the variance of their event-by-event fluctuations. This observation establishes interferometric signatures as useful observable…
The ratio of shear viscosity over entropy density in low energy heavy-ion collision has been calculated by using the Green-Kubo method in the framework of an extended quantum molecular dynamics model. After the system almost reaching a local equilibration for a head-on $^{40}$Ca+$^{100}$Mo collision, thermodynamic and transport properties are extracted. Meanwhile, iso-vector giant dipole resonance (IVGDR) of the collision system is also studied. By the Gaussian fits to the IVGDR photon spectra, the peak energies of IVGDR are extracted at different incident energies. The result shows that the I…
[Background] The "pasta" phase of nuclear matter may play an important role in the structure and evolution of neutron stars. Recent works suggest nuclear pasta has a high resistivity which could be explained by the presence of long lived topological defects. The defects act as impurities that decrease thermal and electrical conductivity of the pasta. [Purpose] To quantify how topological defects affect transport properties of nuclear pasta and estimate this effect using an impurity parameter $Q_{\text{imp}}$. [Methods] Contrast molecular dynamics simulations of up to 409\,600 nucleons arranged…
