37,171 research outputs found
Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model
We derive the renormalized Schwinger-Dyson equations for the one- and
two-point functions in the auxiliary field formulation of
field theory to order 1/N in the 2PI-1/N expansion. We show that the
renormalization of the broken-symmetry theory depends only on the counter terms
of the symmetric theory with . We find that the 2PI-1/N expansion
violates the Goldstone theorem at order 1/N. In using the O(4) model as a low
energy effective field theory of pions to study the time evolution of
disoriented chiral condensates one has to {\em{explicitly}} break the O(4)
symmetry to give the physical pions a nonzero mass. In this effective theory
the {\em additional} small contribution to the pion mass due to the violation
of the Goldstone theorem in the 2-PI-1/N equations should be numerically
unimportant
Machine learning with the hierarchyâofâhypotheses (HoH) approach discovers novel pattern in studies on biological invasions
Research synthesis on simple yet general hypotheses and ideas is challenging in scientific disciplines studying highly contextâdependent systems such as medical, social, and biological sciences. This study shows that machine learning, equationâfree statistical modeling of artificial intelligence, is a promising synthesis tool for discovering novel patterns and the source of controversy in a general hypothesis. We apply a decision tree algorithm, assuming that evidence from various contexts can be adequately integrated in a hierarchically nested structure. As a case study, we analyzed 163 articles that studied a prominent hypothesis in invasion biology, the enemy release hypothesis. We explored if any of the nine attributes that classify each study can differentiate conclusions as classification problem. Results corroborated that machine learning can be useful for research synthesis, as the algorithm could detect patterns that had been already focused in previous narrative reviews. Compared with the previous synthesis study that assessed the same evidence collection based on experts' judgement, the algorithm has newly proposed that the studies focusing on Asian regions mostly supported the hypothesis, suggesting that more detailed investigations in these regions can enhance our understanding of the hypothesis. We suggest that machine learning algorithms can be a promising synthesis tool especially where studies (a) reformulate a general hypothesis from different perspectives, (b) use different methods or variables, or (c) report insufficient information for conducting metaâanalyses
Classical Nucleation Theory of the One-Component Plasma
We investigate the crystallization rate of a one-component plasma (OCP) in
the context of classical nucleation theory. From our derivation of the free
energy of an arbitrary distribution of solid clusters embedded in a liquid
phase, we derive the steady-state nucleation rate of an OCP as a function of
the Coulomb coupling parameter. Our result for the rate is in accord with
recent molecular dynamics simulations, but it is greater than that of previous
analytical estimates by many orders of magnitude. Further molecular dynamics
simulations of the nucleation rate of a supercooled liquid OCP for several
values of the coupling parameter would clarify the physics of this process.Comment: 6 pages, 1 figure, accepted by PR
Monte Carlo calibration of the SMM gamma ray spectrometer for high energy gamma rays and neutrons
The Gamma Ray Spectrometer (GRS) on the Solar Maximum Mission spacecraft was primarily designed and calibrated for nuclear gamma ray line measurements, but also has a high energy mode which allows the detection of gamma rays at energies above 10 MeV and solar neutrons above 20 MeV. The GRS response has been extrapolated until now for high energy gamma rays from an early design study employing Monte Carlo calculations. The response to 50 to 600 MeV solar neutrons was estimated from a simple model which did not consider secondary charged particles escaping into the veto shields. In view of numerous detections by the GRS of solar flares emitting high energy gamma rays, including at least two emitting directly detectable neutrons, the calibration of the high energy mode in the flight model has been recalculated by the use of more sophisticated Monte Carlo computer codes. New results presented show that the GRS response to gamma rays above 20 MeV and to neutrons above 100 MeV is significantly lower than the earlier estimates
Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
We consider the out-of-equilibrium evolution of a classical condensate field
and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a
symmetric and a double well potential. We use the 2PPI formalism and go beyond
the Hartree approximation by including the sunset term. In addition to the mean
field phi= the 2PPI formalism uses as variational parameter a time
dependent mass M**2(t) which contains all local insertions into the Green
function. We compare our results to those obtained in the Hartree
approximation. In the symmetric Phi**4 theory we observe that the mean field
shows a stronger dissipation than the one found in the Hartree approximation.
The dissipation is roughly exponential in an intermediate time region. In the
theory with spontaneous symmetry breaking, i.e., with a double well potential,
the field amplitude tends to zero, i.e., to the symmetric configuration. This
is expected on general grounds: in 1+1 dimensional quantum field theory there
is no spontaneous symmetry breaking for T >0, and so there should be none at
finite energy density (microcanonical ensemble), either. Within the time range
of our simulations the momentum spectra do not thermalize and display
parametric resonance bands.Comment: 14 pages, 18 encapsulated postscript figures; v2 minor changes, new
appendix, accepted for publication in Phys.Rev.
Resumming the large-N approximation for time evolving quantum systems
In this paper we discuss two methods of resumming the leading and next to
leading order in 1/N diagrams for the quartic O(N) model. These two approaches
have the property that they preserve both boundedness and positivity for
expectation values of operators in our numerical simulations. These
approximations can be understood either in terms of a truncation to the
infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a
particular two-particle irreducible vacuum energy graph in the effective action
of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the
case of quantum mechanics where the Lagrangian is . The
key to these approximations is to treat both the propagator and the
propagator on similar footing which leads to a theory whose graphs have the
same topology as QED with the propagator playing the role of the photon.
The bare vertex approximation is obtained by replacing the exact vertex
function by the bare one in the exact Schwinger-Dyson equations for the one and
two point functions. The second approximation, which we call the dynamic Debye
screening approximation, makes the further approximation of replacing the exact
propagator by its value at leading order in the 1/N expansion. These two
approximations are compared with exact numerical simulations for the quantum
roll problem. The bare vertex approximation captures the physics at large and
modest better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are
separately liste
Size of Fireballs Created in High Energy Lead-Lead Collisions as Inferred from Coulomb Distortions of Pion Spectra
We compute the Coulomb effects produced by an expanding, highly charged
fireball on the momentum distribution of pions. We compare our results to data
on Au+Au at 11.6 A GeV from E866 at the BNL AGS and to data on Pb+Pb at 158 A
GeV from NA44 at the CERN SPS. We conclude that the distortion of the spectra
at low transverse momentum and mid-rapidity can be explained in both
experiments by the effect of the large amount of participating charge in the
central rapidity region. By adjusting the fireball expansion velocity to match
the average transverse momentum of protons, we find a best fit when the
fireball radius is about 10 fm, as determined by the moment when the pions
undergo their last scattering. This value is common to both the AGS and CERN
experiments.Comment: Enlarged discussion, new references added, includes new analysis of
pi-/pi+ at AGS energies. 12 pages 5 figures, uses LaTex and epsfi
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
Analytic and Numerical Study of Preheating Dynamics
We analyze the phenomenon of preheating,i.e. explosive particle production
due to parametric amplification of quantum fluctuations in the unbroken case,
or spinodal instabilities in the broken phase, using the Minkowski space
vector model in the large limit to study the non-perturbative issues
involved. We give analytic results for weak couplings and times short compared
to the time at which the fluctuations become of the same order as the tree
level,as well as numerical results including the full backreaction.In the case
where the symmetry is unbroken, the analytic results agree spectacularly well
with the numerical ones in their common domain of validity. In the broken
symmetry case, slow roll initial conditions from the unstable minimum at the
origin, give rise to a new and unexpected phenomenon: the dynamical relaxation
of the vacuum energy.That is, particles are abundantly produced at the expense
of the quantum vacuum energy while the zero mode comes back to almost its
initial value.In both cases we obtain analytically and numerically the equation
of state which turns to be written in terms of an effective polytropic index
that interpolates between vacuum and radiation-like domination. We find that
simplified analysis based on harmonic behavior of the zero mode, giving rise to
a Mathieu equation forthe non-zero modes miss important physics. Furthermore,
analysis that do not include the full backreaction do not conserve energy,
resulting in unbound particle production. Our results do not support the recent
claim of symmetry restoration by non-equilibrium fluctuations.Finally estimates
of the reheating temperature are given,as well as a discussion of the
inconsistency of a kinetic approach to thermalization when a non-perturbatively
large number of particles is created.Comment: Latex file, 52 pages and 24 figures in .ps files. Minor changes. To
appear in Physical Review D, 15 December 199
Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb Gauge
We study the abelian Higgs model out-of-equilibrium in two different
approaches, a gauge invariant formulation, proposed by Boyanovsky et al.
\cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches
become equivalent in a consistent one loop approximation. Furthermore, we carry
out a proper renormalization for the model in order to prepare the equations
for a numerical implementation. The additional degrees of freedom, which arise
in gauge theories, influence the behavior of the system dramatically. A
comparison with results in the 't Hooft-Feynman background gauge found by us
recently, shows very good agreement.Comment: 32 pages, 8 figure
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