4,396 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
Hydrodynamic transport functions from quantum kinetic theory
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu,
Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP),
two-particle-irreducible (2PI) effective action we show how to compute from
first principles the shear and bulk viscosity functions in the
hydrodynamic-thermodynamic regime. For a real scalar field with self-interaction we need to include 4 loop graphs in the equation of
motion. This work provides a microscopic field-theoretical basis to the
``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G.
Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity
reproduces their expression derived from linear response theory and the
imaginary-time formalism of thermal field theory. Though unavoidably involved
in calculations of this sort, we feel that the approach using fundamental
quantum kinetic field theory is conceptually clearer and methodically simpler
than the effective kinetic theory approach, as the success of the latter
requires clever rendition of diagrammatic resummations which is neither
straightforward nor failsafe. Moreover, the method based on the CTP-2PI
effective action illustrated here for a scalar field can be formulated entirely
in terms of functional integral quantization, which makes it an appealing
method for a first-principles calculation of transport functions of a thermal
non-abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion
collisions.Comment: 25 pages revtex, 11 postscript figures. Final version accepted for
publicatio
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
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.
The Role of Nonequilibrium Dynamical Screening in Carrier Thermalization
We investigate the role played by nonequilibrium dynamical screening in the
thermalization of carriers in a simplified two-component two-band model of a
semiconductor. The main feature of our approach is the theoretically sound
treatment of collisions. We abandon Fermi's Golden rule in favor of a
nonequilibrium field theoretic formalism as the former is applicable only in
the long-time regime. We also introduce the concept of nonequilibrium dynamical
screening. The dephasing of excitonic quantum beats as a result of
carrier-carrier scattering is brought out. At low densities it is found that
the dephasing times due to carrier-carrier scattering is in picoseconds and not
femtoseconds, in agreement with experiments. The polarization dephasing rates
are computed as a function of the excited carrier density and it is found that
the dephasing rate for carrier-carrier scattering is proportional to the
carrier density at ultralow densities. The scaling relation is sublinear at
higher densities, which enables a comparison with experiment.Comment: Revised version with additional refs. 12 pages, figs. available upon
request; Submitted to Phys. Rev.
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
Non-Equilibrium Quantum Fields in the Large N Expansion
An effective action technique for the time evolution of a closed system
consisting of one or more mean fields interacting with their quantum
fluctuations is presented. By marrying large expansion methods to the
Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective
action, causality of the resulting equations of motion is ensured and a
systematic, energy conserving and gauge invariant expansion about the
quasi-classical mean field(s) in powers of developed. The general method
is exposed in two specific examples, symmetric scalar \l\F^4 theory
and Quantum Electrodynamics (QED) with fermion fields. The \l\F^4 case is
well suited to the numerical study of the real time dynamics of phase
transitions characterized by a scalar order parameter. In QED the technique may
be used to study the quantum non-equilibrium effects of pair creation in strong
electric fields and the scattering and transport processes in a relativistic
plasma. A simple renormalization scheme that makes practical the
numerical solution of the equations of motion of these and other field theories
is described.Comment: 43 pages, LA-UR-94-783 (PRD, in press), uuencoded PostScrip
Quantum kinetics and thermalization in a particle bath model
We study the dynamics of relaxation and thermalization in an exactly solvable
model of a particle interacting with a harmonic oscillator bath. Our goal is to
understand the effects of non-Markovian processes on the relaxational dynamics
and to compare the exact evolution of the distribution function with
approximate Markovian and Non-Markovian quantum kinetics. There are two
different cases that are studied in detail: i) a quasiparticle (resonance) when
the renormalized frequency of the particle is above the frequency threshold of
the bath and ii) a stable renormalized `particle' state below this threshold.
The time evolution of the occupation number for the particle is evaluated
exactly using different approaches that yield to complementary insights. The
exact solution allows us to investigate the concept of the formation time of a
quasiparticle and to study the difference between the relaxation of the
distribution of bare particles and that of quasiparticles. We derive a
non-Markovian quantum kinetic equation which resums the perturbative series and
includes off-shell effects. A Markovian approximation that includes off-shell
contributions and the usual Boltzmann equation (energy conserving) are obtained
from the quantum kinetic equation in the limit of wide separation of time
scales upon different coarse-graining assumptions. The relaxational dynamics
predicted by the non-Markovian, Markovian and Boltzmann approximations are
compared to the exact result. The Boltzmann approach is seen to fail in the
case of wide resonances and when threshold and renormalization effects are
important.Comment: 39 pages, RevTex, 14 figures (13 eps figures
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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