Fluctuations of the initial color fields in high energy heavy ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^\tau=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.Comment: 36 pages, 5 figures (final version, includes a brief discussion of the numerical implementation

From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on Z2Z^2

In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the algebraic areas over the set of loops that have fixed number of edges in the two directions. We show that these moments are the product of a combinatorial factor that counts the number of such loops, by a polynomial in the numbers of steps in each direction. Our approach leads to an algorithm for obtaining explicit formulas for the moments of low order.Comment: 21 pages, to appear in Annales de l'Institut Henri Poincar\'e

Properties of the Boltzmann equation in the classical approximation

We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.Comment: 37 pages, 21 figure

Instability induced pressure isotropization in a longitudinally expanding system

In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the present paper, we extend this work to a system that expands in the longitudinal direction thereby more closely mimicking a heavy ion collision. We conclude that the microscopic processes that drive the system towards equilibrium are able to keep up with the expansion of the system; the pressure tensor becomes isotropic despite the anisotropic expansion.Comment: revised version to appear in PRD, new section on comparison with hydrodynamics, 32 pages, 21 figure

Progress in Understanding the Nuclear Equation of State at the Quark Level

At the present time there is a lively debate within the nuclear community concerning the relevance of quark degrees of freedom in understanding nuclear structure. We outline the key issues and review the impressive progress made recently within the framework of the quark-meson coupling model. In particular, we explain in quite general terms how the modification of the internal structure of hadrons in-medium leads naturally to three- and four-body forces, or equivalently, to density dependent effective interactions.Comment: Invited presentation at XXX Symposium on Nuclear Physics, Hacienda Cocoyoc, Jan. 3-6, 200

Nuclear Lattice Simulations using Symmetry-Sign Extrapolation

Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal numbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. Here, we introduce the "symmetry-sign extrapolation" method, which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to systematically extend the Projection Monte Carlo calculations to nuclear systems where the sign problem is severe. We benchmark this method by calculating the ground-state energies of the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter.Comment: 25 pages, 12 figures, version to appear in Eur. Phys. J.