No Arabic abstract
In this paper we use the gauge/gravity duality to perform the first systematic study of the onset of hydrodynamic behavior in a hot and dense far-from-equilibrium strongly coupled relativistic fluid with a critical point. By employing a top-down holographic construction that stems from string theory, we numerically obtain the full nonlinear evolution of the far-from-equilibrium system undergoing a Bjorken expansion and address the following question: how does hydrodynamic behavior emerge in the vicinity of a critical point in the phase diagram? For the top-down holographic system analyzed in the present work, we find that the approach to hydrodynamics is strongly affected by the presence of the critical point: the closer the ratio between the chemical potential and the temperature is to its critical value, the longer it takes for the system to be well described by the equations of viscous hydrodynamics.
We compute the homogeneous limit of non-hydrodynamic quasinormal modes (QNMs) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {it quantitatively} describe state-of-the-art lattice results for the QCD equation of state and higher order baryon susceptibilities with $2+1$ flavors and physical quark masses up to highest values of the baryon chemical potential currently reached in lattice simulations; ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion collisions; iii) give a very good description of the bulk viscosity extracted via some recent Bayesian analyzes of hydrodynamical descriptions of heavy ion experimental data. This EMD model has been recently used to predict the location of the QCD critical point in the QCD phase diagram, which was found to be within the reach of upcoming low energy heavy ion collisions. The lowest quasinormal modes of the $SO(3)$ rotationally invariant quintuplet, triplet, and singlet channels evaluated in the present work provide upper bounds for characteristic equilibration times describing how fast the dense medium returns to thermal equilibrium after being subjected to small disturbances. We find that the equilibration times in the different channels come closer to each other at high temperatures, although being well separated at the critical point. Moreover, in most cases, these equilibration times decrease with increasing baryon chemical potential while keeping temperature fixed.
We show that a Bjorken expanding strongly coupled $mathcal{N}=4$ Supersymmetric Yang-Mills plasma can violate the dominant and also the weak energy condition in its approach to hydrodynamics (even though the chosen initial data satisfy these constraints). This suggests that nontrivial quantum effects may be needed to describe the onset of hydrodynamic behavior in heavy-ion collisions. Also, we investigate whether there is an upper bound for the initial entropy of the plasma. We find numerical evidence for such a bound in our simulations and show that close to it the system evolves with approximately zero entropy production at early times, even though it is far from equilibrium.
We use holography to investigate the process of homogeneous isotropization and thermalization in a strongly coupled $mathcal{N} = 4$ Super Yang-Mills plasma charged under a $U(1)$ subgroup of the global $SU(4)$ R-symmetry which features a critical point in its phase diagram. Isotropization dynamics at late times is affected by the critical point in agreement with the behavior of the characteristic relaxation time extracted from the analysis of the lowest non-hydrodynamic quasinormal mode in the $SO(3)$ quintuplet (external scalar) channel of the theory. In particular, the isotropization time may decrease or increase as the chemical potential increases depending on whether one is far or close enough to the critical point, respectively. On the other hand, the thermalization time associated with the equilibration of the scalar condensate, which happens only after the system has relaxed to a (nearly) isotropic state, is found to always increase with chemical potential in agreement with the characteristic relaxation time associated to the lowest non-hydrodynamic quasinormal mode in the $SO(3)$ singlet (dilaton) channel. These conclusions about the late dynamics of the system are robust in the sense that they hold for different initial conditions seeding the time evolution of the far-from-equilibrium plasma.
In the presence of finite chemical potential $mu$, we holographically compute the entanglement of purification in a $2+1$- and $3+1$-dimensional field theory and also in a $3+1$-dimensional field theory with a critical point. We observe that compared to $2+1$- and $3+1$-dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $frac{mu}{T}$ where $T$ is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the dependence of the holographic entanglement of purification on the various parameters of the theories. Moreover, the critical exponent is calculated.
We present new results on the equation of state and transition line of hot and dense strongly interacting QCD matter, obtained from a bottom-up Einstein-Maxwell-Dilaton holographic model. We considerably expand the previous coverage in baryon densities in this model by implementing new numerical methods to map the holographic black hole solutions onto the QCD phase diagram. We are also able to obtain, for the first time, the first-order phase transition line in a wide region of the phase diagram. Comparisons with the most recent lattice results for the QCD thermodynamics are also presented.