4,370 research outputs found
Parallel algorithm with spectral convergence for nonlinear integro-differential equations
We discuss a numerical algorithm for solving nonlinear integro-differential
equations, and illustrate our findings for the particular case of Volterra type
equations. The algorithm combines a perturbation approach meant to render a
linearized version of the problem and a spectral method where unknown functions
are expanded in terms of Chebyshev polynomials (El-gendi's method). This
approach is shown to be suitable for the calculation of two-point Green
functions required in next to leading order studies of time-dependent quantum
field theory.Comment: 15 pages, 9 figure
1+1 Dimensional Compactifications of String Theory
We argue that stable, maximally symmetric compactifications of string theory
to 1+1 dimensions are in conflict with holography. In particular, the finite
horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti de
Sitter space, and of the de Sitter horizon in any dimension, are inconsistent
with the symmetries of these spaces. The argument parallels one made recently
by the same authors, in which we demonstrated the incompatibility of the
finiteness of the entropy and the symmetries of de Sitter space in any
dimension. If the horizon entropy is either infinite or zero the conflict is
resolved.Comment: 11 pages, 2 figures v2: added discussion of AdS_2 and comment
On time-dependent AdS/CFT
We clarify aspects of the holographic AdS/CFT correspondence that are typical
of Lorentzian signature, to lay the foundation for a treatment of
time-dependent gravity and conformal field theory phenomena. We provide a
derivation of bulk-to-boundary propagators associated to advanced, retarded and
Feynman bulk propagators, and provide a better understanding of the boundary
conditions satisfied by the bulk fields at the horizon. We interpret the
subleading behavior of the wavefunctions in terms of specific vacuum
expectation values, and compute two-point functions in our framework. We
connect our bulk methods to the closed time path formalism in the boundary
field theory.Comment: 19 pages, v2: added reference, JHEP versio
Numerical Approximations Using Chebyshev Polynomial Expansions
We present numerical solutions for differential equations by expanding the
unknown function in terms of Chebyshev polynomials and solving a system of
linear equations directly for the values of the function at the extrema (or
zeros) of the Chebyshev polynomial of order N (El-gendi's method). The
solutions are exact at these points, apart from round-off computer errors and
the convergence of other numerical methods used in connection to solving the
linear system of equations. Applications to initial value problems in
time-dependent quantum field theory, and second order boundary value problems
in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate
Neutrino collective excitations in the Standard Model at high temperature
Neutrino collective excitations are studied in the Standard Model at high
temperatures below the symmetry breaking scale. Two parameters determine the
properties of the collective excitations: a mass scale which
determines the \emph{chirally symmetric} gaps in the spectrum and
. The spectrum consists of left handed negative
helicity quasiparticles, left handed positive helicity quasiholes and their
respective antiparticles. For there are two
gapped quasiparticle branches and one gapless and two gapped quasihole
branches, all but the higher gapped quasiparticle branches terminate at end
points. For the quasiparticle spectrum features a
pitchfork bifurcation and for the collective modes are gapless
quasiparticles with dispersion relation below the light cone for
approaching the free field limit for with a rapid crossover
between the soft non-perturbative to the hard perturbative regimes for .The \emph{decay} of the vector bosons leads to a \emph{width} of the
collective excitations of order which is explicitly obtained in the
limits and . At high temperature this damping rate is
shown to be competitive with or larger than the collisional damping rate of
order for a wide range of neutrino energy.Comment: 32 pages 16 figs. Discussion on screening corrections. Results
unchanged to appear in Phys. Rev.
Time evolution of the chiral phase transition during a spherical expansion
We examine the non-equilibrium time evolution of the hadronic plasma produced
in a relativistic heavy ion collision, assuming a spherical expansion into the
vacuum. We study the linear sigma model to leading order in a large-
expansion. Starting at a temperature above the phase transition, the system
expands and cools, finally settling into the broken symmetry vacuum state. We
consider the proper time evolution of the effective pion mass, the order
parameter , and the particle number distribution. We
examine several different initial conditions and look for instabilities
(exponentially growing long wavelength modes) which can lead to the formation
of disoriented chiral condensates (DCCs). We find that instabilities exist for
proper times which are less than 3 fm/c. We also show that an experimental
signature of domain growth is an increase in the low momentum spectrum of
outgoing pions when compared to an expansion in thermal equilibrium. In
comparison to particle production during a longitudinal expansion, we find that
in a spherical expansion the system reaches the ``out'' regime much faster and
more particles get produced. However the size of the unstable region, which is
related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps
On the Derivative Expansion at Finite Temperature
In this short note, we indicate the origin of nonanalyticity in the method of
derivative expansion at finite temperature and discuss some of its
consequences.Comment: 7 pages, UR-1363, ER40685-81
Renormalization of initial conditions and the trans-Planckian problem of inflation
Understanding how a field theory propagates the information contained in a
given initial state is essential for quantifying the sensitivity of the cosmic
microwave background to physics above the Hubble scale during inflation. Here
we examine the renormalization of a scalar theory with nontrivial initial
conditions in the simpler setting of flat space. The renormalization of the
bulk theory proceeds exactly as for the standard vacuum state. However, the
short distance features of the initial conditions can introduce new divergences
which are confined to the surface on which the initial conditions are imposed.
We show how the addition of boundary counterterms removes these divergences and
induces a renormalization group flow in the space of initial conditions.Comment: 22 pages, 4 eps figures, uses RevTe
Strong Dissipative Behavior in Quantum Field Theory
We study under which conditions an overdamped regime can be attained in the
dynamic evolution of a quantum field configuration. Using a real-time
formulation of finite temperature field theory, we compute the effective
evolution equation of a scalar field configuration, quadratically interacting
with a given set of other scalar fields. We then show that, in the overdamped
regime, the dissipative kernel in the field equation of motion is closely
related to the shear viscosity coefficient, as computed in scalar field theory
at finite temperature. The effective dynamics is equivalent to a time-dependent
Ginzburg-Landau description of the approach to equilibrium in phenomenological
theories of phase transitions. Applications of our results, including a
recently proposed inflationary scenario called ``warm inflation'', are
discussed.Comment: 45 pages, 5 figures, Latex, In press Phys. Rev. D, minor correction
High-field noise in metallic diffusive conductors
We analyze high-field current fluctuations in degenerate conductors by
mapping the electronic Fermi-liquid correlations at equilibrium to their
semiclassical non-equilibrium form. Our resulting Boltzmann description is
applicable to diffusive mesoscopic wires. We derive a non-equilibrium
connection between thermal fluctuations of the current and resistive
dissipation. In the weak-field limit this is the canonical fluctuation-
dissipation theorem. Away from equilibrium, the connection enables explicit
calculation of the excess ``hot-electron'' contribution to the thermal
spectrum. We show that excess thermal noise is strongly inhibited by Pauli
exclusion. This behaviour is generic to the semiclassical metallic regime.Comment: 13 pp, one fig. Companion paper to cond-mat/9911251. Final version,
to appear in J. Phys.: Cond. Ma
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