A scaling relation between pA and AA collisions

We compare the flow-like correlations in high multiplicity proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions. At fixed multiplicity, the correlations in these two colliding systems are strikingly similar, although the system size is smaller in $p+A$. Based on an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $p+A$ emerges as a collective response to the fluctuations in the position of clusters, just like in $A+A$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $p+A$ collisions. We also explore the implications of the model for jet energy loss in $p+A$, and predict slightly larger transverse momentum broadening in $p+A$ than in $A+A$ at the same multiplicity.

Plane correlations and hydrodynamic simulations of heavy ion collisions

We use a nonlinear response formalism to describe the event plane correlations measured by the ATLAS collaboration. With one exception ($leftlangle cos(2Psi_2 - 6Psi_3 + 4 Psi_4) rightrangle$), the event plane correlations are qualitatively reproduced by considering the linear and quadratic response to the lowest cumulants. For the lowest harmonics such as $leftlangle cos(2Psi_2+3Psi_3 - 5Psi_5) rightrangle$, the correlations are quantitatively reproduced, even when the naive Glauber model prediction has the wrong sign relative to experiment. The quantitative agreement for the higher plane correlations (especially those involving $Psi_6$) is not as good. The centrality dependence of the correlations is naturally explained as an average of the linear and quadratic response.

Second order viscous corrections to the harmonic spectrum in heavy ion collisions

We calculate the second order viscous correction to the kinetic distribution, $delta f_{(2)}$, and use this result in a hydrodynamic simulation of heavy ion collisions to determine the complete second order correction to the harmonic spectrum, $v_n$. At leading order in a conformal fluid, the first viscous correction is determined by one scalar function, $chi_{0p}$. One moment of this scalar function is constrained by the shear viscosity. At second order in a conformal fluid, we find that $delta f(p)$ can be characterized by two scalar functions of momentum, $chi_{1p}$ and $chi_{2p}$. The momentum dependence of these functions is largely determined by the kinematics of the streaming operator. Again, one moment of these functions is constrained by the parameters of second order hydrodynamics, $tau_pi$ and $lambda_1$. The effect of $delta f_{(2)}$ on the integrated flow is small (up to $v_4$), but is quite important for the higher harmonics at modestly-large $p_T$. Generally, $delta f_{(2)}$ increases the value of $v_n$ at a given $p_T$, and is most important in small systems.

Fluctuation, dissipation, and thermalization in non-equilibrium AdS_5 black hole geometries

We give a simple recipe for computing dissipation and fluctuations (commutator and anti-commutator correlation functions) for non-equilibrium black hole geometries. The recipe formulates Hawking radiation as an initial value problem, and is suitable for numerical work. We show how to package the fluctuation and dissipation near the event horizon into correlators on the stretched horizon. These horizon correlators determine the bulk and boundary field theory correlation functions. In addition, the horizon correlators are the components of a horizon effective action which provides a quantum generalization of the membrane paradigm. In equilibrium, the analysis reproduces previous results on the Brownian motion of a heavy quark. Out of equilibrium, Wigner transforms of commutator and anti-commutator correlation functions obey a fluctuation-dissipation relation at high frequency.

Triangularity and Dipole Asymmetry in Heavy Ion Collisions

We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity $<r^3 cos3(phi - psi_{3,3})>$ and the dipole asymmetry $<r^3 cos(phi- psi_{1,3})>$ of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry $psi_{1,3}$ has a $20%$ preference out of plane. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles $psi_{1,3}$ and $psi_{3,3}$ are strongly correlated. We study the ideal hydrodynamic response to these cumulants and determine the associated $v_1/epsilon_1$ and $v_3/epsilon_3$ for a massless ideal gas equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and Roland fit of two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole asymmetry and the correlations between $psi_{1,3}$ and $psi_{3,3}$ by measuring a two particle correlation with respect to the participant plane, $<cos(phi_a - 3phi_b + 2Psi_{PP})>$. The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, $<cos(phi_a + phi_b - 2Psi_{PP})>$.

Spectral densities for hot QCD plasmas in a leading log approximation

We compute the spectral densities of $T^{mu u}$ and $J^{mu}$ in high temperature QCD plasmas at small frequency and momentum,, $omega,k sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a second order diffusion equation. We determine all of the second order transport coefficients which characterize the linear response in the hydrodynamic regime.