624 research outputs found
Quarkonia and Heavy-Quark Relaxation Times in the Quark-Gluon Plasma
A thermodynamic T-matrix approach for elastic 2-body interactions is employed
to calculate spectral functions of open and hidden heavy-quark systems in the
Quark-Gluon Plasma. This enables the evaluation of quarkonium bound-state
properties and heavy-quark diffusion on a common basis and thus to obtain
mutual constraints. The two-body interaction kernel is approximated within a
potential picture for spacelike momentum transfers. An effective
field-theoretical model combining color-Coulomb and confining terms is
implemented with relativistic corrections and for different color channels.
Four pertinent model parameters, characterizing the coupling strengths and
screening, are adjusted to reproduce the color-average heavy-quark free energy
as computed in thermal lattice QCD. The approach is tested against vacuum
spectroscopy in the open (D, B) and hidden (Psi and Upsilon) flavor sectors, as
well as in the high-energy limit of elastic perturbative QCD scattering.
Theoretical uncertainties in the static reduction scheme of the 4-dimensional
Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are
used to calculate Euclidean correlators which are discussed in light of lattice
QCD results, while heavy-quark relaxation rates and diffusion coefficients are
extracted utilizing a Fokker-Planck equation.Comment: 33 pages, 28 figure
Fixed-Angle Elastic Hadron Scattering
The scattering amplitude in the dual model with Mandelstam analyticity and
trajectory is studied in the limit By
using the saddle point method, a series decomposition for the scattering
amplitude is obtained, with the leading and two sub-leading terms calculated
explicitly.Comment: 15 pages, LaTeX, 2 figures with eps file
Convergence rate for a curse-ofdimensionality-free method for a class of HJB PDEs
Abstract. In previous work of the first author and others, max-plus methods have been explored for solution of firstorder, nonlinear Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods can provide substantial computationalspeed advantages, they still generally suffer from the curse-of-dimensionality. Here we consider HJB PDEs where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. The approach to solution will be rather general, but in order to ground the work, we consider only constituent Hamiltonians corresponding to long-run averagecost-per-unit-time optimal control problems for the development. We consider a previously obtained numerical method not subject to the curse-of-dimensionality. The method is based on construction of the dual-space semigroup corresponding to the HJB PDE. This dual-space semigroup is constructed from the dual-space semigroups corresponding to the constituent linear/quadratic Hamiltonians. The dual-space semigroup is particularly useful due to its form as a max-plus integral operator with kernel obtained from the originating semigroup. One considers repeated application of the dual-space semigroup to obtain the solution. Although previous work indicated that the method was not subject to the curse-of-dimensionality, it did not indicate any error bounds or convergence rate. Here, we obtain specific error bounds. Key words. partial differential equations, curse-of-dimensionality, dynamic programming, max-plus algebra, Legendre transform, Fenchel transform, semiconvexity, Hamilton-Jacobi-Bellman equations, idempotent analysis. AMS subject classifications. 49LXX, 93C10, 35B37, 35F20, 65N99, 47D99 1. Introduction. A robust approach to the solution of nonlinear control problems is through the general method of dynamic programming. For the typical class of problems in continuous time and continuous space, with the dynamics governed by finite-dimensional, ordinary differential equations, this leads to a representation of the problem as a first-order, nonlinear partial differential equation, the Hamilton-Jacobi-Bellman equation -or the HJB PDE. If one has an infinite time-horizon problem, then the HJB PDE is a steady-state equation, and this PDE is over a space (or some subset thereof) whose dimension is the dimension of the state variable of the control problem. Due to the nonlinearity, the solutions are generally nonsmooth, and one must use the theory of viscosity solution
Gauge Dependence in Chern-Simons Theory
We compute the contribution to the modulus of the one-loop effective action
in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We
find that the results are dependent on both the gauge parameter () and
the metric required in the gauge fixing. A contribution arises that has not
been previously encountered; it is of the form . This is possible as in three dimensions
is dimensionful. A variant of proper time regularization is used to render
these integrals well behaved (although no divergences occur when the
regularization is turned off at the end of the calculation). Since the original
Lagrangian is unaltered in this approach, no symmetries of the classical theory
are explicitly broken and is handled unambiguously
since the system is three dimensional at all stages of the calculation. The
results are shown to be consistent with the so-called Nielsen identities which
predict the explicit gauge parameter dependence using an extension of BRS
symmetry. We demonstrate that this dependence may potentially
contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty
(available from LANL). Latex thric
On the notion of potential in quantum gravity
The problem of consistent definition of the quantum corrected gravitational
field is considered in the framework of the -matrix method. Gauge dependence
of the one-particle-reducible part of the two-scalar-particle scattering
amplitude, with the help of which the potential is usually defined, is
investigated at the one-loop approximation. The -terms in the potential,
which are of zero order in the Planck constant are shown to be
independent of the gauge parameter weighting the gauge condition in the action.
However, the -terms, proportional to describing the first
proper quantum correction, are proved to be gauge-dependent. With the help of
the Slavnov identities, their dependence on the weighting parameter is
calculated explicitly. The reason the gauge dependence originates from is
briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure
The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC
We investigate the production of hadrons in nuclear collisions within the
framework of the thermal (or statistical hadronization) model. We discuss both
the ligh-quark hadrons as well as charmonium and provide predictions for the
LHC energy. Even as its exact magnitude is dependent on the charm production
cross section, not yet measured in Pb-Pb collisions, we can confidently predict
that at the LHC the nuclear modification factor of charmonium as a function of
centrality is larger than that observed at RHIC and compare the experimental
results to these predictions.Comment: 4 pages, 3 figures; proceedings of QM201
Quark Matter and Nuclear Collisions: A Brief History of Strong Interaction Thermodynamics
The past fifty years have seen the emergence of a new field of research in
physics, the study of matter at extreme temperatures and densities. The theory
of strong interactions, quantum chromodynamics (QCD), predicts that in this
limit, matter will become a plasma of deconfined quarks and gluons -- the
medium which made up the early universe in the first 10 microseconds after the
big bang. High energy nuclear collisions are expected to produce short-lived
bubbles of such a medium in the laboratory. I survey the merger of statistical
QCD and nuclear collision studies for the analysis of strongly interacting
matter in theory and experiment.Comment: 24 pages, 14 figures Opening Talk at the 5th Berkeley School on
Collective Dynamics in High Energy Collisions, LBNL Berkeley/California, May
14 - 18, 201
Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives
Contribution of matter fields to the Gell-Mann-Low function for N=1
supersymmetric Yang-Mills theory, regularized by higher covariant derivatives,
is obtained using Schwinger-Dyson equations and Slavnov-Tailor identities. A
possible deviation of the result from the corresponding contribution in the
exact Novikov, Shifman, Vainshtein and Zakharov -function is discussed.Comment: 20 pages, 4 figure
Gauge dependence of effective gravitational field
The problem of gauge independent definition of effective gravitational field
is considered from the point of view of the process of measurement. Under
assumption that dynamics of the measuring apparatus can be described by the
ordinary classical action, effective Slavnov identities for the generating
functionals of Green functions corresponding to a system of arbitrary
gravitational field measured by means of scalar particles are obtained. With
the help of these identities, the total gauge dependence of the non-local part
of the one-loop effective apparatus action, describing the long-range quantum
corrections, is calculated. The value of effective gravitational field inferred
from the effective apparatus action is found to be gauge-dependent. A probable
explanation of this result, referring to a peculiarity of the gravitational
interaction, is given.Comment: Revised version as publishe
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