161 research outputs found
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 shortly after the collision, in the
Fock-Schwinger gauge .
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
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 C, He and 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.
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