We consider QCD near but above critical temperature Tc. The pressure, susceptibilities and the renormalized Polyakov loop -- which is an order parameter for the deconfining phase transition -- dramatically change up to temperatures a few times Tc. We refer to this region as a "semi"-QGP, where partial confinement plays important role. We show that the shear viscosity ,eta, is suppressed by two powers of the Polyakov loop. This suggests that eta/T^3 decreases markedly as QCD cools down to temperatures near Tc. We also show a ratio of the viscosity to the entropy becomes small near Tc.
We discuss shear viscosity of the quark matter by using Kubo formula. The shear viscosity is calculated in the framework of the quasi-particle RPA for the Nambu-Jona-Lasinio model. We obtain a formula that the shear viscosity is expressed by the quadratic form of the quark spectral function in the chiral symmetric phase. The magnitude of the shear viscosity is discussed assuming the Breit-Wigner type for the spectral function.
We discuss the shear viscosity of the quark matter by using the Kubo-Mori formula. It is found that the shear viscosity is expressed in terms of the quark spectral function. If the spectral function is approximated by a modified Bright-Wigner type, the viscosity decreases as the width of the spectral function increases. We also discuss dependence of the shear viscosity on the temperature and the density.
We calculate shear viscosity of the quark matter at finite temperature and density. If we assume that the quark interacts with the soft mode, which is a collective mode of quark-antiquark pair, the self energy of the quark is calculated by using the quasi-particle random phase approximation. It is shown that its imaginary part is large and the mean free path of the quark is short. With the use of the Kubo formula, the shear viscosity of quark matter becomes small. The Reynolds number of the quark matter is estimated to be about $3\sim 30$. As the temperature increases, the shear viscosity incr…
We study the Anderson Localization effect on the shear viscosity in a system with random medium by Kubo formula. We show that this effect can reduce the shear viscosity nonperturbatively. Then we discuss its possible implementation in heavy-ion collisions, where the created heavy bound states or other collective modes may play the role of the random scatterer underlying Anderson Localization effect.
The shear viscosity is calculated by means of the perturbative kinetic partonic cascade BAMPS with CGC initial conditons for various saturation momentum scale Q_s. eta/s ~ 0.15 stays approximately constant when going from RHIC to LHC.
Shear viscosity is a dynamical property of fluid systems close to equilibrium, describing resistance to sheared flow. After reviewing the physics of viscosity and the reason it is usually difficult to compute, I discuss its importance within the theory of QCD and the obstacles to carrying out such a computation. A diagrammatic analysis requires extensive resummations and even then convergence is poor at physically relevant couplings. Lattice approaches require a poorly controlled analytical continuation of data from the Euclidean to the Minkowski domain. At present our best results for QCD she…
In this article we calculate the leading order shear viscosity in QCD using the resummed 3PI effective action. We work to 3-loop order in the effective action. We show that the integral equations that resum the pinching and collinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.
Within the framework of finite temperature field theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths(damping rates) are introduced to regulate the pinch singularities. The finite chemical potential, which enhances the contributions to the shear viscosity from the electrons while suppresses those from the photons, finally gives a positive contribution compared to the pure temperature environment. The result agrees with that from the kinetics theory qualitatively.
Using the standard Green-Kubo formalism, we determine the shear viscosity $η$ of a hot and dense Yukawa-Fermi gas. In particular, we study the effect of particle and plasmino excitations on thermal properties of the fermionic part of the shear viscosity, and explore the effects of thermal corrections to particle masses on bosonic and fermionic shear viscosities, $η_b$ and $η_f$. It turns out that the effects of plasminos on $η_f$ become negligible with increasing (decreasing) temperature (chemical potential).
The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential $μ$, despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite $μ$, and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should…
We investigate the effects of baryon chemical potential μon the shear viscosity coefficient ηand the viscosity to entropy density ratio η/s of a pion-nucleon gas mixture. We find that ηis an increasing function of T and μ, while the ratio η/s turns to a decreasing function in a wide region of T-μplane. In the kinematical region we studied, the smallest value of η/s is about 0.3.
We model the soft pomeron contribution to dipole-dipole scattering as a closed string exchange in AdS5 with a wall. The exchange of closed and long strings is characterized by an apparent Unruh temperature and entropy that are caused by the rapidity interval chi of the collision. We show that the primordial transverse shear viscosity to transverse entropy density ratio is eta-perp/s-perp=(pi k/chi)^2/(8 pi) for scattering dipoles of N-ality k, vanishing at large chi.
We consider the shear viscosity of a system of quarks and its ratio to the entropy density above the critical temperature for deconfinement. Both quantities are derived and computed for different modeling of the quark self-energy, also allowing for a temperature dependence of the effective mass and width. The behaviour of the viscosity and the entropy density is argued in terms of the strength of the coupling and of the main characteristics of the quark self-energy. A comparison with existing results is also discussed.
Shear viscosity of the gluon plasma in SU(3) YM theory is calculated nonperturbatively, within the stochastic vacuum model. The result for the ratio of the shear viscosity to the entropy density, proportional to the squared chromo-magnetic gluon condensate and the fifth power of the correlation length of the chromo-magnetic vacuum, falls off with the increase of temperature. At temperatures larger than the deconfinement critical temperature by a factor of 2, this fall-off is determined by the sixth power of the temperature-dependent strong-coupling constant and yields an asymptotic approach to…
Fast thermalization and elliptic flow of QCD matter found at the Relativistic Heavy Ion Collider (RHIC) are understood as the consequence of perturbative QCD (pQCD) interactions within a (3+1) dimensional parton cascade. The main contributions stem from pQCD-inspired bremsstrahlung. We extract the shear viscosity to entropy ratio, which is between 0.08 and 0.15.
In the framework of irreversible thermodynamics, we studied the transport properties of QGP. Shear viscosity and non-equilibrium entropy density related to viscous process at finite density has been investigated in weakly coupled limit by using kinetic theory. The results show that the chemical potential increases viscosityyet decreases the non-equilibrium entropy density and thus contributes positively to their ratio compared to the pure temperature case. As to the temperature dependence of the ratio, the ratio first decreases rapidly and then increases in the physical region, presenting a mi…
We show that the shear viscosity of lambda phi^4 theory is sensitive at next-to-leading order to soft physics, which gives rise to subleading corrections suppressed by only a half power of the coupling, eta = [3033.54 + 1548.3 m_{th}/T] N T^3]/[ (N+2)/3 lambda^2], with m^2_th=(N+2)/72 lambda T^2. The series appears to converge about as well (or badly) as the series for the pressure.
The shear viscosity of an interacting pion gas is studied using the Kubo formalism as a microscopic description of thermal systems close to global equilibrium. We implement the skeleton expansion in order to approximate the retarded correlator of the viscous part of the energy-momentum tensor. After exploring this in $gϕ^4$ theory we show how the skeleton expansion can be consistently applied to pions in chiral perturbation theory. The shear viscosity $η$ is determined by the spectral width, or equivalently, the mean free path of pions in the heat bath. We derive a new analytical result for th…
Within the framework of relativistic fluctuating hydrodynamics we compute the contribution of thermal fluctuations to the effective infrared shear viscosity of a conformal fluid, focusing on quadratic (in fluctuations), second order (in velocity gradients) terms in the conservation equations. Our approach is based on the separation of hydrodynamic fields in soft and ultrasoft sectors, in which the effective shear viscosity arises due to the action of the soft modes on the evolution of the ultrasoft ones. We find that for a strongly coupled fluid with small shear viscosity--to--entropy ratio $η…
One of the most remarkable features of the Quark Gluon Plasma is its nearly perfect fluidity behavior indicated by the small shear viscosity to entropy density ratio obtained from fitting relativistic viscous hydrodynamics flow harmonics to experimental data. In recent years, bulk viscosity has also been considered in the context of event-by-event relativistic hydrodynamics and it has been found to have a non-trivial interplay with shear viscosity. In this paper some of the issues are discussed that require further work when extracting the shear viscosity to entropy density ratio in the presen…
The interplay between shear and bulk viscosities on the flow harmonics, $v_n$'s, at RHIC is investigated using the newly developed relativistic 2+1 hydrodynamical code v-USPhydro that includes bulk and shear viscosity effects both in the hydrodynamic evolution and also at freeze-out. While shear viscosity is known to attenuate the flow harmonics, we find that the inclusion of bulk viscosity decreases the shear viscosity-induced suppression of the flow harmonics bringing them closer to their values in ideal hydrodynamical calculations. Depending on the value of the bulk viscosity to entropy den…
We consider an effective field theory description of beyond-quasi-particle excitations aiming to associate the transport properties of the system with the spectral density of states. Tuning various properties of the many-particle correlations, we investigate how the robust microscopic features are translated into the macroscopic observables like shear viscosity and entropy density. The liquid-gas crossover is analysed using several examples. A thermal constraint on the fluidity measure, the ratio of shear viscosity to entropy density, is discussed.
The shear viscosity bound violation in Einstein gravity for anisotropic black branes is discussed, with the aim of constraining the deviation of the shear viscosity-entropy density ratio from the shear viscosity bound using causality and thermodynamics analysis. The results show that no stringent constraints can be imposed. The diffusion bound in anisotropic phases is also studied. Ultimately, it is concluded that shear viscosity violation always occurs in cases where the equation of motion of the metric fluctuations cannot be written in a form identical to that of the minimally coupled massle…
We derive an analytic expression for the shear viscosity of an ultra-relativistic gas in presence of both elastic $2\to 2$ and inelastic $2\leftrightarrow 3$ processes with isotropic differential cross sections. The derivation is based on the entropy principle and Grad's approximation for the off-equilibrium distribution function. The obtained formula relates the shear viscosity coefficient $η$ to the total cross sections $σ_{22}$ and $σ_{23}$ of the elastic resp. inelastic processes. The values of shear viscosity extracted using the Green-Kubo formula from kinetic transport calculations are s…
We investigate the shear viscosity of neutron star matter in the presence of an antikaon condensate. The electron and muon number densities are reduced due to the appearance of a $K^-$ condensate in neutron star matter, whereas the proton number density increases. Consequently the shear viscosity due to scatterings of electrons and muons with themselves and protons is lowered compared to the case without the condensate. On the other hand, the contribution of proton-proton collisions to the proton shear viscosity through electromagnetic and strong interactions, becomes important and comparable …
The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the pQCD based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3-8 compared to elastic scatterings. The shear viscosity scales with the coupling as 1/(alpha_s^2\log(1/alpha_s)). For a constant coupling constant the shear viscosity to entropy density ratio …
We calculate the shear viscosity $η$ of a quark plasma through the two-flavor Nambu-Jona-Lasinio (NJL) model in the chiral limit, at finite temperature $T$, and baryon number chemical potential $μ_B$. We solve the Boltzmann equation by using in the collision term cross sections that are correct to leading order in the coupling constant. We find the ratio of shear viscosity to entropy density above and slightly below the chiral transition temperature to vary from 1.5 to 13 times the conjectured lower bound of $(4π)^{-1}$ depending on the chemical potential to temperature ratio. Ratio of shear v…
The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio η/s for a gluon gas, which involves elastic gg-> gg perturbative QCD (PQCD) scatterings as well as inelastic gg<->ggg PQCD bremsstrahlung. For α_s=0.3 we find η/s=0.13 and for α_s=0.6, η/s=0.076. The small η/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.
We have calculated the shear viscosity of pion medium, where propagating pion has some finite thermal width due to interaction with the low mass resonances, $σ$ and $ρ$. With the help of standard thermal field theoretical technique, the thermal width of the pion has been calculated from the pion self-energy diagram for $πσ$ and $πρ$ loops, where an effective Lagrangian density has been used for interaction part. We have found a very small value of shear viscosity by entropy density ratio ($η/s$), which is very close to the KSS bound.
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 …
Starting from a classical picture of shear viscosity we construct a stationary velocity gradient in a microscopic parton cascade. Employing the Navier-Stokes ansatz we extract the shear viscosity coefficient $η$. For elastic isotropic scatterings we find an excellent agreement with the analytic values. This confirms the applicability of this method. Furthermore for both elastic and inelastic scatterings with pQCD based cross sections we extract the shear viscosity coefficient $η$ for a pure gluonic system and find a good agreement with already published calculations.
We present the first calculation of the shear viscosity for two-flavor plane wave (FF) color superconducting quark matter. This is a member of the family of crystalline color superconducting phases of dense quark matter that may be present in the cores of neutron stars. The paired quarks in the FF phase feature gapless excitations on surfaces of crescent shaped blocking regions in momentum space and participate in transport. We calculate their contribution to the shear viscosity. We note that they also lead to dynamic screening of transverse $t^1$, $t^2$, $t^3$ gluons which are undamped in the…
It is well known that the difference between the chemical potentials of left-handed and right-handed particles in a parity violating (chiral) plasma can lead to an instability. We show that the chiral instability may drive turbulent transport. Further we estimate the anomalous viscosity of chiral plasma arising from the enhanced collisionality due to turbulence.
We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: $eB\sim g^4\log(1/g)T^2$. We show that the shear viscosity takes a form $η=\barη(\bar B)T^3/(g^4\log(1/g))$ with a dimensionless function $\barη(\bar B)$ in terms of a dimensionless variable $\bar B=(eB)/(g^4\log(1/g)T^2)$. The variable $\bar B$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $\bar B\sim l_{mfp}/l_{cyclo}$. We provide a full numerical result for t…
We have computed shear viscosity coefficient for hot and dense QCD matter within Polyakov loop extended quark meson(PQM) model for three flavors. Viscosity coefficient is estimated using Boltzmann equation within the relaxation time approximation. Relaxation times for quarks are calculated from elastic scattering of quarks and antiquarks via gluon exchange. Also the mean free paths of strange and light quarks are estimated for this cases. The calculations are performed at finite chemical potential. Thermodynamic properties like energy, pressure, entropy densities are also computed and compared…
We have evaluated the shear viscosity of pion gas taking into account its scattering with the low mass resonances, $σ$ and $ρ$ during propagation in the medium. The thermal width (or collisional rate) of the pions is calculated from $πσ$ and $πρ$ loop diagrams using effective interactions in the real time formulation of finite temperature field theory. A very small value of shear viscosity by entropy density ratio ($η/s$), close to the KSS bound, is obtained which approximately matches the range of values of $η/s$ used by Niemi et al. \cite{Niemi} in order to fit the RHIC data of elliptic flow…
The lower bound of the shear viscosity to entropy density ratio is examined using an exact representation of the ratio through the density of states. It is shown that the lower bound in a generic physical system is not universal, its value is determined by the entropy density. Some examples of physical systems are discussed in the paper where one can expect violation of the conformal 1/4pi value.
We estimate bulk and shear viscosity at finite temperature and baryon densities of hadronic matter within hadron resonance gas model. For bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For shear viscosity coefficient, we estimate the same using molecular kinetic theory to relate the shear viscosity coefficient to average momentum of the hadrons in the hot and dense hadron gas. The bulk viscosity to entropy ratio increases with chemical potential and is related to the reduction of velocity of sound at nonzero chemical potential. The shear viscosity …
The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.
The fireball concept of Rolf Hagedorn, developed in the 1960's, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes …
Shear viscosity ηand entropy density s of a hadronic resonance gas are calculated using the Chapman-Enskog and virial expansion methods using the K-matrix parametrization of hadronic cross sections which preserves the unitarity of the T -matrix. In the π-K-N-η- mixture considered, a total of 57 resonances up to 2 GeV were included. Comparisons are also made to results with other hadronic cross sections such as the Breit-Wigner (BW) and, where available, experimental phase shift parametrizations. Hadronic interactions forming resonances are shown to decrease the shear viscosity and increase the…
In a recent Letter [Phys. Rev. Lett. 114 091301 (2105)] the cause of the acceleration of the present Universe has been identified with the shear viscosity of an imperfect relativistic fluid even in the absence of any bulk viscous contribution. The gist of this comment is that the shear viscosity, if anything, can only lead to an accelerated expansion over sufficiently small scales well inside the Hubble radius.
Gauge theory - gravity duality predicts that the shear viscosity of N=4 supersymmetric SU(N_c) Yang-Mills plasma at temperature T in the limit of large N_c and large 't Hooft coupling g^2_{YM} N_c is independent of the coupling and equals to πN_c^2 T^3/8. In this paper, we compute the leading correction to the shear viscosity in inverse powers of 't Hooft coupling using the α'-corrected low-energy effective action of type IIB string theory. We also find the correction to the ratio of shear viscosity to the volume entropy density (equal to 1/4πin the limit of infinite coupling). The correction …
Experiments at the Relativistic Heavy Ion Collider (RHIC) suggest that the state of matter produced in the experiments has a low shear-viscosity to entropy-density ratio. We ask here the question what is this ratio in usual finite nuclei at low temperature. We use the experimental and theoretical results for the widths of giant vibrational states in nuclei in order to calculate the above ratio. We find that the values of this ratio are not very different from the ones found in the RHIC experiments.
We calculate for the first time the shear viscosity of ultrarelativistic Boson systems in the presence of a Bose-Einstein condensate (BEC). Two different methods are used. One is the Grad's method of moments and another is the Green-Kubo relation within a kinetic transport approach. In this work we consider a Boson system with isotropic elastic collisions and a gluon system with elastic scatterings described by perturbation QCD (pQCD). The results show that the presence of a BEC lowers the shear viscosity. This effect becomes stronger for the increasing proportion of the BEC in the Boson syste…
We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $η/s$. The point-like interaction rates of hadrons are evaluated through the $S$-matrix approach in the presence of a magnetic field to obtain the temperature and magnetic field-dependent relaxation time. We observe that the transport coefficients are anisotropic in the presence of the magnetic field. We calculate the temperature and magnetic field-dependent anisotropi…
We analyze the contributions of Nambu-Goldstone modes to the shear viscosity of a superfluid atomic Fermi gas close to unitarity. We show that the low temperature experimental values of the shear viscosity to entropy ratio, $η/s$, are reproduced considering an effective shear viscosity which takes into account the collisions among Nambu-Goldstone bosons and the finite size of the optical trap. We predict that, for $T \lesssim 0.1 T_F$, $η/s$ should correlate with the size of the trap and linearly decrease with decreasing temperature. For $T \gtrsim 0.1 T_F$, we find agreement with the experime…
We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature T limit the shear viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the chemical potential and the Fermi energy, mu=xi E_F. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature T_c. A naive extrapola…
We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections -- that is, corrections suppressed by one power of $g$ relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring $η/s$ down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at $T \simeq 100$ GeV. The largest next-to-leading order correction to $η/s$ arises from modifications to the qhat parameter, which determines the rate of transverse momentum diffusion. …
We compute the shear viscosity of weakly coupled N=4 supersymmetric Yang-Mills (SYM) theory. Our result for [eta/s], the viscosity to entropy-density ratio, is many times smaller than the corresponding weak-coupling result in QCD. This suggests that [eta/s] of QCD near the transition point is several times larger than the viscosity bound, [eta/s] >= 1/4 pi.
The chromo-electromagnetic field fluctuations in the quark-gluon plasma (QGP) play an important role as these field fluctuations result energy gain of heavy quarks. We consider these fluctuations and evaluate the transport coefficients, e.g., drag and diffusion coefficients of charm quarks and shear viscosity to entropy density ratio ($η/s$) of the QGP. We find a significant effect of such fluctuations on the transport coefficients. These fluctuations cause a reduction of the drag and diffusion coefficients. We also observe that the shear viscosity to entropy density ratio of the QGP is closer…
We compute the shear viscosity in the O(N) model at first nontrivial order in the large N expansion. The calculation is organized using the 1/N expansion of the 2PI effective action (2PI-1/N expansion) to next-to-leading order, which leads to an integral equation summing ladder and bubble diagrams. We also consider the weakly coupled theory for arbitrary N, using the three-loop expansion of the 2PI effective action. In the limit of weak coupling and vanishing mass, we find an approximate analytical solution of the integral equation. For general coupling and mass, the integral equation is solve…
We study evolution of quark-gluon matter in the ultrarelativistic heavy-ion collisions within the frame work of relativistic second-order viscous hydrodynamics. In particular, by using the various prescriptions of a temperature-dependent shear viscosity to the entropy ratio, we show that the hydrodynamic description of the relativistic fluid become invalid due to the phenomenon of cavitation. For most of the initial conditions relevant for LHC, the cavitation sets in very early during the evolution of the hydrodynamics in time $\lesssim 2 $fm/c. The cavitation in this case is entirely driven b…
In this article, we will briefly review the recent progress on hydrodynamic modeling and the extraction of the quark-gluon plasma (QGP) specific shear viscosity with an emphasis on results obtained from the hybrid model VISHNU that couples viscous hydrodynamics for the macroscopic expansion of the QGP to the hadron cascade model for the microscopic evolution of the late hadronic stage.
We investigate the shear viscosity $η$ of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. Dependence of the shear viscosity $η(g,T)$ on the coupling $g$ and temperature $T$ is represented by a scaling function $f_η(g^2T)$ as $η(g,T)=Tf_η(g^2T)$ due to the scaling-invariant property of the CYM. The explicit functional form of $f_η(g^2T)$ is successfully determined from the calculated shear viscosity: It turns out that $η(g,T)$ of the CYM fie…
The gravitational formfactor similar to shear viscosity is identified. In the time-like region it corresponds to the contribution of exotic hybrid meson. The exotic quantum numbers may be considered as a counterpart of dissipation in crossed channel. The ratio of viscosity to entropy density is estimated. The smallness due to holographic bound corresponds to the relative smallness of coupling of hybrid meson and the intrinsic transverse momentum, being the dynamical counterpart of temperature.
We compute the energy and momentum deposited by a fast moving parton in a quark-gluon plasma using linear viscous hydrodynamics with an energy loss per unit length profile proportional to the path length and with different values of the shear viscosity to entropy density ratio. We show that when varying these parameters, the transverse modes still dominate over the longitudinal ones and thus energy and momentum is preferentially deposited along the head-shock, as in the case of a constant energy loss per unit length profile and the lowest value for the shear viscosity to entropy density ratio.
