121,860 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
Brunnian Braids and Lie Algebras
Brunnian braids have interesting relations with homotopy groups of spheres.
In this work, we study the graded Lie algebra of the descending central series
related to Brunnian subgroup of the pure braid group. A presentation of this
Lie algebra is obtained.Comment: 21 page
Real-time multiple-look synthetic aperture radar processor for spacecraft applications
A spaceborne synthetic aperture radar (SAR) having pipeline multiple-look data processing is described which makes use of excessive azimuth bandwidth in radar echo signals to produce multiple-looking images. Time multiplexed single-look image lines from an azimuth correlator go through an energy analyzer which analyzes the mean energy in each separate look to determine the radar antenna electric boresight for use in generating the correct reference functions for the production of high quality SAR images. The multiplexed single look image lines also go through a registration delay to produce multi-look images
Apparatus for determining changes in limb volume
Measuring apparatus for determining changes in the volume of limbs or other boty extremities by determining the cross-sectional area of such limbs many comprise a transmitter including first and second transducers for positioning on the surface of the limb at a predetermined distance there between, and a receiver including a receiver crystal for positioning on the surface of the limb. The distance between the receiver crystal and the first and second transducers are represented by respective first and second chords of the cross-section of the limb and the predetermined distance between the first and second transducers is represented by a third chord of the limb cross section
Basis-conjugating automorphisms of a free group and associated Lie algebras
Let F_n = denote the free group with generators {x_1,...,x_n}.
Nielsen and Magnus described generators for the kernel of the canonical
epimorphism from the automorphism group of F_n to the general linear group over
the integers. In particular among them are the automorphisms chi_{k,i} which
conjugate the generator x_k by the generator x_i leaving the x_j fixed for j
not k. A computation of the cohomology ring as well as the Lie algebra obtained
from the descending central series of the group generated by chi_{k,i} for i<k
is given here. Partial results are obtained for the group generated by all
chi_{k,i}.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Regulation and the neo-Wicksellian approach to monetary policy
Laubach and Williams (2003) employ a Kalman filter approach to jointly estimate the neutral real federal funds rate and trend output growth using an IS relationship and an output gap based inflation equation. They find a positive link between these two variables, but also much error surrounding neutral real rate estimates. We modify their approach by including variables for regulations on deposit interest rates and on wages and prices. These variables are statistically significant and notably affect estimates of two policy relevant coefficients: the sensitivity of output to the real interest rate and that of inflation to the output gap.Monetary policy ; Federal funds rate
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