Within a covariant parton cascade, we discuss the impact of both finite shear viscosity $η$ and freeze-out dynamics on the elliptic flow generated at RHIC. We find that the enhancement of $η/s$ in the cross-over region of the QGP phase transition cannot be neglected in order to extract the information from the QGP phase. We also point out that the elliptic flow $v_2(p_T)$ for a fluid at $η/s \sim 0.1-0.2$ is consistent with the one needed by quark number scaling drawing a nice consistency between the nearly perfect fluid property of QGP and the coalescence process.
In this article, we briefly review the recent progress related to extracting the quark-gluon plasma (QGP) specific shear viscosity from the flow data measured at Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC).
Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared to Navier Stokes.
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 show from covariant transport theory that, for a massless ideal gas equation of state, even a small shear viscosity to entropy density ratio $η\approx s/(4 π)$ generates significant 15-30% dissipative corrections to elliptic flow for conditions expected in mid-peripheral (b = 8 fm) Au+Au collisions at $\sqrt{s_{NN}} \sim 200$ GeV at RHIC.
We study the effects of bulk viscosity on p_T spectra and elliptic flow in heavy ion collisions at RHIC. We argue that direct effect of the bulk viscosity on the evolution of the velocity field is small, but corrections to the freezeout distributions can be significant. These effects are dominated by chemical non-equilibration in the hadronic phase. We show that a non-zero bulk viscosity in the range $ζ/s \lsim 0.05$ improves the description of spectra and flow at RHIC.
A variety of physical phenomena can lead to viscous effects. In this talk we review several sources of shear and bulk viscosity with an emphasis on the bulk viscosity associated with chiral restoration. We show that in the limit of a second order phase transition, the viscosity peaks in a singularity at the critical point.
A variety of physical phenomena can lead to viscous effects. Several sources of shear and bulk viscosity are reviewed with an emphasis on the bulk viscosity associated with chiral restoration and with chemical non-equilibrium. We show that in a mean-field treatment of the limiting case of a second order phase transition, the bulk viscosity peaks in a singularity at the critical point.
Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.
We consider the longitudinal hydrodynamic evolution of the fireball created in a relativistic heavy-ion collision. Nonzero shear viscosity reduces the colling rate of the system and hinders the acceleration of the longitudinal flow. As a consequence, the initial energy density needed to reproduce the experimental data at RHIC energies is significantly reduced. At LHC energies, we expect that shear viscosity helps to conserve a Bjorken plateau in the rapidity distributions during the expansion.
We study real photons produced in heavy ion collisions at RHIC, and we calculate their spectrum and its azimuthal momentum anisotropy. The photons from a variety of sources are included, and the interplay and the time-evolution of those sources are modelled in a full 3D hydrodynamic simulation. We quantify the v_2 of thermal photons produced in ideal and viscous fluids, and the consequences of using different initial conditions are explored.
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.
Within a Boltzmann transport model, we demonstrate correlation between stopping observables and shear viscosity in central nuclear collisions at intermediate energies (on the order of 10 to 1000 MeV/nucleon). The correlation allows us to assess the viscosity of nuclear matter, by tuning the in-medium nucleon-nucleon cross section in our transport model to agree with nuclear stopping data. We also calculate the ratio of shear viscosity to entropy density to determine how close the system is to the universal quantum lower limit proposed in the context of ultrarelativistic heavy ion collisions.
We report recent progress on causal viscous hydrodynamics for relativistic heavy ion collisions. For fixed specific shear viscosity eta/s, uncertainties in the elliptic flow arising from initial conditions, equation of state, bulk viscosity and numerical viscosity, and the treatment of the highly viscous hadronic stage and freeze-out procedure are analysed. A comparison of current viscous hydrodynamic results with experimental data yields a robust upper limit eta/s < 5/(4pi).
Within the improved quantum molecular dynamic (ImQMD) model we follow the evolution of nuclear matter for planar Couette flow in a periodic box. We focus on the region of liquid-gas phase transition and extract the shear viscosity coefficient from the local stress tensor, directly following viscosity definition. By switching on and off the mean field and thus inducing the phase transition, we are able to observe the impact of clumping in the phase-transition region onto the viscosity.
The specific shear viscosity (eta/s)_QGP of quark-gluon plasma (QGP) can be extracted from elliptic flow data in heavy-ion collisions by comparing them with the dynamical model VISHNU which couples a viscous fluid dynamic description of the QGP with a microscopic kinetic description of the late hadronic rescattering and freeze-out stage. A robust method for fixing (eta/s)_QGP from the collision centrality dependence of the eccentricity-scaled charged hadron elliptic flow is presented. The systematic uncertainties associated with this extraction method are discussed, with specific attention to …
Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for sqrt{s}=200 GeV Au+Au collisions are presented. For Glauber-type initial conditions, while data on integrated v_2 is consistent with a ratio of viscosity over entropy density up to eta/s=0.16, data on minimum bias v_2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.
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.
In this talk I report my recent study on the shear viscosity of neutron-rich nuclear matter from a relaxation time approach. An isospin- and momentum-dependent interaction is used in the study. Effects of density, temperature, and isospin asymmetry of nuclear matter on its shear viscosity have been discussed. Similar to the symmetry energy, the symmetry shear viscosity is defined and its density and temperature dependence are studied.
We extract the specific shear viscosity $η/s$ of nuclear matter for various temperatures and chemical potentials in the hadronic phase using data taken in high energy nuclear collisions. We use a blastwave parameterization of the final state of nuclear collisions, including non-equilibrium deformations of particle distributions due to shear stress in the Navier-Stokes approximation. We fit spectra and elliptic flow of identified hadrons for a variety of collision energies and impact parameters at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The systems analyz…
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.
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…
This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $η/s (T)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $η/s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.
The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $η$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $η/s$ of shear viscosity $η$ to entropy density $s$ is extracted from the experimental systematics of the GDR in copper, tin and lead isotopes at finite temperature $T$. These empirical results are then compared with the predictions by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the r…
We evaluate the shear viscosity of a pion gas in the relativistic kinetic theory approach. The in-medium propagator of the $ρ$ meson at finite temperature is used to evaluate the $π-π$ scattering amplitude in the medium. The real and imaginary parts of the self-energy calculated from one-loop diagrams are seen to have noticeable effects on the scattering cross-section. The consequences on temperature dependence of the shear viscosity evaluated in the Chapman-Enskog and relaxation time approximations are studied.
Elliptic flow measurements at RHIC suggest that quark gluon plasma flows with very little viscosity compared to weak coupling expectations, challenging theorists to explain why this fluid is so nearly ``perfect''. It is therefore vital to find quantitative experimental information on the viscosity of the plasma. We propose that measurements of transverse momentum fluctuations can be used to determine the shear viscosity. We use current data to estimate the viscosity-to-entropy ratio in the range from 0.08 to 0.3, and discuss how future measurements can reduce this uncertainty.
Viscosity plays a critical role in determining the stability of rotating neutron stars. We report the results of a calculation of the shear viscosity of $β$~-~stable matter, carried out using an effective interaction based on a state-of-the-art nucleon-nucleon potential and the formalism of correlated basis functions. Within our approach the equation of state, determining the proton fraction, and the nucleon-nucleon scattering probability are consistently obtained from the same dynamical model. The results show that, while the neutron contribution to the viscosity is always dominant, above nuc…
Based on an improved isospin- and momentum-dependent interaction, we have studied the qualitative effect of isospin splitting of nucleon effective mass on the specific shear viscosity of neutron-rich nuclear matter from a relaxation time approach. It is seen that for $m_n^\star>m_p^\star$, the relaxation time of neutrons is smaller and the neutron flux between flow layers is weaker, leading to a smaller specific shear viscosity of neutron-rich matter compared to the case for $m_n^\star<m_p^\star$. The effect is larger in nuclear matter at higher densities, lower temperatures, and larger isospi…
In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times, respectively. They are found by examining response functions of the stress-energy tensor. We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode. We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of …
We revisit the membrane paradigm calculations of the holographic shear viscosity tensor of strongly coupled isotropic plasmas with Einstein gravity dual by emphasizing the fact which was overlooked in the previous literatures that the shear viscosity is a fourth-rank tensor. Using the membrane paradigm we show that depending on whether the holographic shear viscosity tensor to entropy density ratio is η^j_i^j_i/s or η^{jiji}/s or η_{jiji}/s, we can derive three distinct formulae for the holographic shear viscosity tensor to entropy density ratios given explicitly in terms of the background met…
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 …
We analyze how recent computations of the shear viscosity $η$ in the core of superfluid neutron stars affect the r-mode instability window. We first analyze the contribution of superfluid phonons to the viscosity, both in their hydrodynamical and ballistic regime. We also consider the recent computation of $η$ arising from the collisions of electrons with electrons and protons by Shternin and Yakovlev, and discuss how the interactions among superfluid phonons and electrons might contribute to the shear viscosity. For assessing the r-mode instability window we compare the shear viscosity due to…
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 kaonic contribution to the shear viscosity of quark matter in the kaon-condensed color-flavor locked phase (CFL-K0). This contribution comes from a light pseudo-Goldstone boson which arises from the spontaneous breaking of the flavor symmetry by the kaon condensate. The other contribution, from the exactly massless superfluid 'phonon", has been calculated previously. We specialize to a particular form of the interaction lagrangian, parameterized by a single coupling. We find that if we make reasonable guesses for the values of the parameters of the effective theory, the kaons …
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…
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.
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.
The electron shear viscosity due to Coulomb scattering of degenerate electrons by atomic nuclei throughout a magnetized neutron star crust is calculated. The theory is based on the shear viscosity coefficient calculated neglecting magnetic fields but taking into account gaseous, liquid and solid states of atomic nuclei, multiphonon scattering processes, and finite sizes of the nuclei albeit neglecting the effects of electron band structure. The effects of strong magnetic fields are included in the relaxation time approximation with the effective electron relaxation time taken from the field-fr…
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…
We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=nλ^3/2$ is small. Here, $n$ is the density of the gas and $λ$ is the thermal wave length of the fermions. At leading order in the fugacity expansion the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order medium effects modify the scattering amplitude as well …
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 …
We investigate a first-order phase transition from hadronic matter to antikaon condensed matter during the cooling stage of protoneutron stars. The phase transition proceeds through the thermal nucleation of antikaon condensed matter. In this connection we study the effect of shear viscosity on the thermal nucleation rate of droplets of antikaon condensed matter. Here we adopt the same equation of state for the calculation of shear viscosity and thermal nucleation time. We compute the shear viscosity of neutron star matter composed of neutrons, protons, electrons and muons using the relativist…
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…
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.
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 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. and measurements of the equation of state by Ku et al. We find that the shear viscosity to particle density ratio just above the critical temperature is $η/n|_{T_c}=0.41\pm 0.11$. We also obtain evidence that the shear viscosity to entropy density ratio has a …
We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a non-trivial dilaton using AdS/CFT. We find that the dilaton filed has a non-trivial contribution to the ratio of shear viscosity over entropy density and after imposing causal constraint for the boundary field theory, the new lower bound $4/25π$, obtained from pure Gauss-Bonnet gravity, may have a small violation.
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 study holographic RG flow of the shear viscosity tensor of anisotropic, strongly coupled N=4 super-Yang-Mills plasma by using its type IIB supergravity dual in anisotropic bulk spacetime. We find that the shear viscosity tensor has three independent components in the anisotropic bulk spacetime away from the boundary, and one of the components has a non-trivial RG flow while the other two have a trivial one. For the component of the shear viscosity tensor with non-trivial RG flow, we derive its RG flow equation, and solve the equation analytically to second order in the anisotropy parameter …
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 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 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.
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…
We present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with the bound for the shear viscosity originating from hydrodynamic fluctuations. Assuming smoothness of the frequency dependent shear viscosity eta(omega), we show that the bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper paring in the system. In order to preserve the hydrodynamic bound in QMC eta(omega) has…
