The onset of fluid-dynamical behavior in relativistic kinetic theory

In this proceedings we discuss recent findings regarding the large order behavior of the Chapman-Enskog expansion in relativistic kinetic theory. It is shown that this series in powers of the Knudsen number has zero radius of convergence in the case of a Bjorken expanding fluid described by the Boltzmann equation in the relaxation time approximation. This divergence stems from the presence of non-hydrodynamic modes, which give non-perturbative contributions to the Knudsen series.Comment: 4 pages, 1 figure, proceedings for Quark Matter 201

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.Comment: 22 pages, 7 figure

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2⊗S2\mathrm{AdS}_{2}\otimes \mathrm{S}_{2}

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime $\mathrm{AdS}_{2}\otimes \mathrm{S}_{2}$. We further derive explicit analytic expressions for the momentum dependence of the single particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The non-equilibrium contribution to the entropy density is shown to be due to higher order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Thus, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, non-hydrodynamical microscopic degrees of freedom that lead to entropy production.Comment: 17 pages, 2 figures; added reference, version accepted for publication in Phys. Rev.

Debye screening mass near deconfinement from holography

In this paper the smallest thermal screening mass associated with the correlator of the $CT$-odd operator, $\sim {\rm Tr}F_{\mu\nu}\tilde{F}^{\mu\nu}$, is determined in strongly coupled non-Abelian gauge plasmas which are holographically dual to non-conformal, bottom-up Einstein+scalar gravity theories. These holographic models are constructed to describe the thermodynamical properties of $SU(N_c)$ plasmas near deconfinement at large $N_c$ and we identify this thermal mass with the Debye screening mass $m_D$. In this class of non-conformal models with a first order deconfinement transition at $T_c$, $m_D/T$ displays the same behavior found for the expectation value of the Polyakov loop (which we also compute) jumping from zero below $T_c$ to a nonzero value just above the transition. In the case of a crossover phase transition, $m_D/T$ has a minimum similar to that found for the speed of sound squared $c_s^2$. This holographic framework is also used to evaluate $m_D$ as a function of $\eta/s$ in a strongly coupled conformal gauge plasma dual to Gauss-Bonnet gravity. In this case, $m_D/T$ decreases with increasing $\eta/s$ in accordance with extrapolations from weak coupling calculations.Comment: 48 pages, 16 figures, updated reference

Transient Fluid Dynamics of the Quark-Gluon Plasma According to AdS/CFT

We argue, using the AdS/CFT correspondence, that the transient dynamics of the shear stress tensor in a strongly coupled $\mathcal{N}=4$ SYM plasma is not described by relaxation-type, fluid dynamical equations: at long times the equations of motion should contain a \textit{second-order} comoving derivative of the shear stress tensor. This occurs because in this strongly-coupled system the lowest "non-hydrodynamical" quasinormal modes associated with shear stress possess a nonzero real part at zero wavenumber. We use Weyl invariance to obtain the most general equations of motion containing 2 comoving derivatives of the shear stress tensor in the transient regime that are compatible with the symmetries. We show that the asymptotic solution of this theory valid at times much larger than the timescale associated with the "non-hydrodynamical" modes reproduces the well-known results previously obtained directly from the AdS/CFT correspondence. If the QGP formed in heavy ion collisions can be at least qualitatively understood in terms of strongly-coupled $\mathcal{N}=4$ SYM theory, the second time derivative present in the equations of motion of the fluid may lead to an unexpected dependence on the initial conditions for the shear stress tensor needed in numerical hydrodynamic simulations.Comment: 11 pages, 1 figure: major changes in the text were made in order to clarify the discussio

Bulk Viscosity Effects in Event-by-Event Relativistic Hydrodynamics

Bulk viscosity effects on the collective flow harmonics in heavy ion collisions are investigated, on an event by event basis, using a newly developed 2+1 Lagrangian hydrodynamic code named v-USPhydro which implements the Smoothed Particle Hydrodynamics (SPH) algorithm for viscous hydrodynamics. A new formula for the bulk viscous corrections present in the distribution function at freeze-out is derived starting from the Boltzmann equation for multi-hadron species. Bulk viscosity is shown to enhance the collective flow Fourier coefficients from $v_2(p_T)$ to $v_5(p_T)$ when $$ GeV even when the bulk viscosity to entropy density ratio, $$, is significantly smaller than $1/(4\pi)$.Comment: 23 pages, 12 figures, corrected typos, one reference include

Elliptic Flow Suppression due to Hadron Mass Spectrum

Hadron resonance gas models provide a good description of the equation of state of quantum chromodynamics determined by lattice QCD calculations at temperatures $T \sim 100-155$ MeV. In this paper we investigate the effects of an exponentially increasing hadron mass spectrum (Hagedorn spectrum) on the azimuthal anisotropy of the rapidly expanding matter formed in ultrarelativistic heavy ion collisions. If the temperature at which the conversion from fluid degrees of freedom to hadrons is sufficiently close to the Hagedorn temperature, the production of Hagedorn resonances suppresses the differential elliptic flow of all hadron species.Comment: 6 pages, 3 figures, improved discussion, added references, to appear in Physical Review

Large Nc Deconfinement Transition in the Presence of a Magnetic Field

We investigate the effect of a homogeneous magnetic field on the thermal deconfinement transition of QCD in the large $N_c$ limit. First we discuss how the critical temperature decreases due to the inclusion of $N_f \ll N_c$ flavors of massless quarks. Then we study the equivalent correction in the presence of an external Abelian magnetic field. To leading order in $N_{f}/N_{c}$, the fact that the deconfinement critical temperature decreases with the magnetic field depends solely on quarks behaving paramagnetically. Finally, we discuss the effects from a finite quark mass and its competition with magnetic effects.Comment: 5 pages, 1 figure; v2: version accepted for publication in Phys. Rev.

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity

A new approach is described to help improve the foundations of relativistic viscous fluid dynamics and its coupling to general relativity. Focusing on neutral conformal fluids constructed solely in terms of hydrodynamic variables, we derive the most general viscous energy-momentum tensor yielding equations of motion of second order in the derivatives, which is shown to provide a novel type of generalization of the relativistic Navier-Stokes equations for which causality holds. We show how this energy-momentum tensor may be derived from conformal kinetic theory. We rigorously prove existence, uniqueness, and causality of solutions of this theory (in the full nonlinear regime) both in a Minkowski background and also when the fluid is dynamically coupled to Einstein's equations. Linearized disturbances around equilibrium in Minkowski spacetime are stable in this causal theory. A numerical study reveals the presence of an out-of-equilibrium hydrodynamic attractor for a rapidly expanding fluid. Further properties are also studied and a brief discussion of how this approach can be generalized to non-conformal fluids is presented.Comment: 33 pages, 5 figures. Substantial improvements were made: the new conformal tensor is now derived from kinetic theory; the causality and well-posedness theorems now hold under more general conditions on the transport coefficients; further discussion and applications have also been included; new references were adde

On the fluid behavior of a baryon rich hadron resonance gas

We investigate the effects of finite baryon chemical potential on the transport properties of a hadron resonance gas. We find that a hadron resonance gas with large baryon number density is closer to the ideal fluid limit than the corresponding gas with zero baryon number. This suggests that the system created at the Relativistic Heavy Ion Collider (RHIC) at lower collision energies may behave as a fluid, with an effective fluidity close to the one found at RHIC's highest energy near phase transition. This might explain why the differential elliptic flow coefficient measured at lower collisional energies at RHIC is similar to the one observed at high energies.Comment: 8 pages, 8 figure