Early Time Evolution of High Energy Heavy Ion Collisions

We solve the Yang-Mills equations in the framework of the McLerran-Venugopalan model for small times tau after a collision of two nuclei. An analytic expansion around tau=0 leads to explicit results for the field strength and the energy momentum tensor of the gluon field at early times. We then discuss constraints for the energy density, pressure and flow of the plasma phase that emerges after thermalization of the gluon field.Comment: 4 pages, 1 figure; contribution to Quark Matter 2006; submitted to J. Phys.

Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions

Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as $p_L/p_T = -[1-\frac{3}{2a}(Q\tau)^2]/[1-\frac{1}{a}(Q\tau)^2]+\mathcal{O}(Q\tau)^4$ where $\tau$ is the longitudinal proper time, $Q$ is related to the saturation scales $Q_s$ of the two nuclei, and $a = \ln (Q^2/\hat{m}^2)$ with $\hat m$ a scale to be defined later. Our results are generally applicable if $\tau \lesssim 1/Q$. As already discussed in a previous paper, the transverse energy flow $S^i$ of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density $\nabla^i \varepsilon$. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.Comment: 26 pages, 9 figure

From Color Fields to Quark Gluon Plasma

We discuss a model for the energy distribution and the early space-time evolution of a heavy ion collision. We estimate the gluon field generated in the wake of hard processes and through primordial fluctuations of the color charges in the nuclei. Without specifying the dynamical mechanism of thermalization we calculate the energy momentum tensor of the following plasma phase. The results of this model can be used as initial conditions for a further hydrodynamic evolution.Comment: Contribution to Quark Matter 2005; 4 pages, 4 figure

High Energy Nuclear Collisions: Theory Overview

We review some basic concepts of Relativistic Heavy Ion Physics and discuss our understanding of some key results from the experimental program at the Relativistic Heavy Ion Collider (RHIC). We focus in particular on the early time dynamics of nuclear collisions, some result from lattice QCD, hard probes and photons.Comment: 11 pages, 3 figures; delivered at ISNP 2009, published in Praman

Stable Generalized Finite Element Method (SGFEM)

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution of the associated linear system. In this paper, we address this issue and propose a modification of the GFEM, referred to as the Stable GFEM (SGFEM). We show that the conditioning of the stiffness matrix of SGFEM is not worse than that of the standard FEM. Moreover, SGFEM is very robust with respect to the parameters of the enrichments. We show these features of SGFEM on several examples.Comment: 51 pages, 4 figure

Chemical composition of the decaying glasma

The the initial stage of a relativistic heavy ion collision can be described by a classical color field configuration known as the Glasma. The production of quark pairs from this background field is then computed nonperturbatively by numerically solving the Dirac equation in the classical background. The result seems to point towards an early chemical equilibration of the plasma.Comment: 8 pages, 5 figures, invited talk at Stangeness in Quark Matter 2006 (SQM06), UCLA, March 200

The QCD confinement transition: hadron formation

We review the foundations and the applications of the statistical and the quark recombination model as hadronization models.Comment: 45 pages, 16 figures, accepted for publication in Landolt-Boernstein Volume 1-23