Abstract:
Fluctuations are one of the main probes of the physics of the new state of hot and dense nuclear matter called the Quark Gluon Plasma (QGP) which is created in the ultra-relativistic heavy ion collisions. In this dissertation we extend and improve upon the existing descriptions of heavy ion collisions in three different directions: we study the new signatures of initial state fluctuations, the propagation of perturbations in the early stages of the collision, and the effect of thermal fluctuations on the hydrodynamic expansion of the QGP. First, in Chapter 3 we study initial state fluctuations by examining the complete statistical information contained in the two-particle correlation measurements in hydrodynamic simulations of Pb+Pb collisions at the CERN Large Hadron Collider ( âˆšs_NN = 2.76 TeV). We use Principal Component Analysis (PCA) to decompose the spectrum of harmonic flow, v_n(p_T) for n = 0â€“5, into dominant components. The leading component is identified with the standard event plane v_n(p_T), while the subleading component describes additional fluctuations in the two-particle correlation function. We find good geometric predictors for the orientation and the magnitude of the leading and the subleading flows. The subleading v_0 , v_1 , and v_3 flow harmonics are shown to be a response to the radial excitation of the corresponding eccentricity Îµ_n . In contrast, for v_2 the subleading flow in peripheral collisions is dominated by the nonlinear mixing between the leading elliptic flow and radial flow fluctuations. Nonlinear mixing also plays a significant role in generating subleading v_4 and v_5 harmonics. The PCA gives a systematic way of studying the full information of the two-particle correlation matrix and identifying the subleading flows, which we show are responsible for factorization breaking in hydrodynamics. Second, in Chapter 4 we study the thermalization and hydrodynamization of fluctuations at the early stages of heavy ion collisions. We use leading order effective kinetic theory, accurate at weak coupling, to simulate the pre-equilibrium evolution of transverse energy and flow perturbations. For the short evolution we can use a linear response theory to construct the pre-equilibrium Green functions. Then the energy-momentum tensor at a time when hydrodynamics becomes applicable can be expressed as a linear convolution of response functions with the initial perturbations. We propose combining effective kinetic theory with weak coupling initial state models, such as IP-Glasma, to model the complete pre-thermal evolution from saturated nuclei to hydrodynamics in a weak coupling framework. Last, in Chapter 5 we consider out-of-equilibrium hydrodynamic fluctuations in the expanding QGP. We develop a set of kinetic equations for a correlator of thermal fluctuations which are equivalent to nonlinear hydrodynamics with noise. We first show that the kinetic response precisely reproduces the one-loop renormalization of the shear viscosity for a static fluid. We then use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion. The steady state solution to the kinetic equations determine the coefficient of the first fractional power of the gradient expansion (âˆ 1/(Ï„ T)^(3/2) ), which was computed here for the first time. The formalism of hydro-kinetic equations can be applied to more general background flows and coupled to existing viscous hydrodynamic codes to incorporate the physics of hydrodynamic fluctuations.