9,500 research outputs found
Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism
We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in
perturbative QCD. Employing the formalism, we calculate the two-point gluon
correlation function due to the lowest-order classical
gluon fields in the McLerran-Venugopalan model of heavy ion collisions and
observe an interesting transition from the classical fields to the
quasi-particle picture at later times. Motivated by this observation, we push
the formalism to higher orders in the coupling and calculate the contribution
to coming from the diagrams representing a single
rescattering between two of the produced gluons. We assume that the two gluons
go on mass shell both before and after the rescattering. The result of our
calculation depends on the ordering between the proper time of the rescattering
and the proper time when the gluon distribution is measured.
For (i) and (with the saturation
scale) we obtain the same results as from the Boltzmann equation. For (ii)
we end up with a result very different from
kinetic theory and consistent with a picture of "free-streaming" particles. Due
to the approximations made, our calculation is too coarse to indicate whether
the ordering (i) or (ii) is the correct one: to resolve this controversy, we
shall present a detailed diagrammatic calculation of the rescattering
correction in the theory in the second paper of this duplex.Comment: 45 pages, 9 figure
Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the Theory
To understand the dynamics of thermalization in heavy ion collisions in the
perturbative framework it is essential to first find corrections to the
free-streaming classical gluon fields of the McLerran-Venugopalan model. The
corrections that lead to deviations from free streaming (and that dominate at
late proper time) would provide evidence for the onset of isotropization (and,
possibly, thermalization) of the produced medium. To find such corrections we
calculate the late-time two-point Green function and the energy-momentum tensor
due to a single scattering process involving two classical fields. To
make the calculation tractable we employ the scalar theory instead
of QCD. We compare our exact diagrammatic results for these quantities to those
in kinetic theory and find disagreement between the two. The disagreement is in
the dependence on the proper time and, for the case of the two-point
function, is also in the dependence on the space-time rapidity : the
exact diagrammatic calculation is, in fact, consistent with the free streaming
scenario. Kinetic theory predicts a build-up of longitudinal pressure, which,
however, is not observed in the exact calculation. We conclude that we find no
evidence for the beginning of the transition from the free-streaming classical
fields to the kinetic theory description of the produced matter after a single
rescattering.Comment: 46 pages, 9 figure
Thermodynamics of an accelerated expanding universe
We investigate the laws of thermodynamics in an accelerating universe driven
by dark energy with a time-dependent equation of state. In the case we consider
that the physically relevant part of the Universe is that envelopped by the
dynamical apparent horizon, we have shown that both the first law and second
law of thermodynamics are satisfied. On the other hand, if the boundary of the
Universe is considered to be the cosmological event horizon the thermodynamical
description based on the definitions of boundary entropy and temperature breaks
down. No parameter redefinition can rescue the thermodynamics laws from such a
fate, rendering the cosmological event horizon unphysical from the point of
view of the laws of thermodynamics.Comment: 13 pages, 2 figure
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