Heavy ion collisions quickly form a droplet of quark-gluon plasma (QGP) with a remarkably small viscosity. We give an accessible introduction to how to study this smallest and hottest droplet of liquid made on earth and why it is so interesting. The physics of heavy ions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales. These gluons quickly thermalize and form QGP, while the energetic partons traverse this plasma and end in a shower of particles called jets. Analyzing the final particles in a variety of different ways allows us to study the properties of QGP and the complex dynamics of multi-scale processes in QCD which govern its formation and evolution, providing what is perhaps the simplest form of complex quantum matter that we know of. Much remains to be understood, and throughout the review big open questions will be encountered. 2Busza, Rajagopal and van der Schee to be 1.65±0.1 TeV (4), meaning that the average energy density 1 fm/c after the collision is greater than 1.65 TeV/(π(7 fm) 2 (0.92 fm)) = 12 GeV/fm 3 , about twenty times the energy density of a hadron. The entropy produced in these collisions is also enormous; to get a sense of this note that before the collision the entropy of the two incident nuclei is essentially zero whereas the final state after the collision can contain as many as 30,000 particles, and hence has a very large entropy. We shall return to this later, and in particular we shall see that most of this entropy is produced quickly, in the initial moments after the collision. To get a further sense of the magnitude of the average energy density 1 fm/c after the collision, note that, as we shall see in Section 3, lattice calculations of QCD thermodynamics show that matter in thermal equilibrium at a temperature of 300 MeV has an energy density ≈ 12 T 4 = 12.7 GeV/fm 3 . Thus, the quarks and gluons produced in the collision cannot be described as a collection of distinct individual hadrons. Nevertheless, the quarks and gluons www.annualreviews.org • HIC: The Big Picture and Big Questions 3 4 Busza, Rajagopal and van der Schee 20 Busza, Rajagopal and van der Schee

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a cross-over between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around mid-rapidity is not approximately boost-invariant but Gaussian, albeit with a width that increases with the collision energy.

We study the isotropization of a homogeneous, strongly coupled, non-abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full nonlinear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of the order of t(iso)≲1/T, with T the final equilibrium temperature. We comment on possible extensions to less symmetric situations.

We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti-de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.

Abstract:The holographic isotropization of a highly anisotropic, homogeneous, strongly coupled, non-Abelian plasma was simplified in ref.[1] by linearizing Einstein's equations around the final, equilibrium state. This approximation reproduces the expectation value of the boundary stress tensor with a 20% accuracy. Here we elaborate on these results and extend them to observables that are directly sensitive to the bulk interior, focusing for simplicity on the entropy production on the event horizon. We also consider next-toleading-order corrections and show that the leading terms alone provide a better description of the isotropization process for the states that are furthest from equilibrium.

The understanding of heavy ion collisions and its quark-gluon plasma formation requires a complicated interplay of rich physics in a wealth of experimental data. In this work we compare for identified particles the transverse momentum dependence of both the yields and the anisotropic flow coefficients for both PbPb and pPb collisions. We do this in a global model fit including a free streaming prehydrodynamic phase with variable velocity v fs , thereby widening the scope of initial conditions. During the hydrodynamic phase we vary three second order transport coefficients. The free streaming velocity has a preference slightly below the speed of light. In this extended model the bulk viscosity is small and even consistent with zero.

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity v fs and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and pPb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an outof-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of the system.