704 research outputs found
Plasticity and learning in a network of coupled phase oscillators
A generalized Kuramoto model of coupled phase oscillators with slowly varying
coupling matrix is studied. The dynamics of the coupling coefficients is driven
by the phase difference of pairs of oscillators in such a way that the coupling
strengthens for synchronized oscillators and weakens for non-synchronized
pairs. The system possesses a family of stable solutions corresponding to
synchronized clusters of different sizes. A particular cluster can be formed by
applying external driving at a given frequency to a group of oscillators. Once
established, the synchronized state is robust against noise and small
variations in natural frequencies. The phase differences between oscillators
within the synchronized cluster can be used for information storage and
retrieval.Comment: 10 page
Nonsingular instantons for the creation of open universes
We show that the instability of the singular Vilenkin instanton describing
the creation of an open universe can be avoided using, instead of a minimally
coupled scalar field, an axionic massless scalar field which gives rise to the
Giddings-Strominger instanton. However, if we replace the singularity of the
Hawking Turok instanton for an axionic wormhole some interpretational and
technical difficulties would appear which can be overcome by introducing a
positive cosmological constant in the action. This would make the instanton
finite and free constant in the action. This would make the instanton finite
and free from any instabilities.Comment: 8 pages, RevTex. A new section on the instantonic global structure
and a figure have been added. To appear in Phys. Rev.
Relativistic calculation of nuclear transparency in (e,e'p) reactions
Nuclear transparency in (e,e'p) reactions is evaluated in a fully
relativistic distorted wave impulse approximation model. The relativistic mean
field theory is used for the bound state and the Pauli reduction for the
scattering state, which is calculated from a relativistic optical potential.
Results for selected nuclei are displayed in a Q^2 range between 0.3 and 1.8
(GeV/c)^2 and compared with recent electron scattering data. For Q^2 = 0.3
(GeV/c)^2 the results are lower than data; for higher Q^2 they are in
reasonable agreement with data. The sensitivity of the model to different
prescriptions for the one-body current operator is investigated. The off-shell
ambiguities are rather large for the distorted cross sections and small for the
plane wave cross sections.Comment: 8 pages, 3 figure
Nucleon Charge and Magnetization Densities from Sachs Form Factors
Relativistic prescriptions relating Sachs form factors to nucleon charge and
magnetization densities are used to fit recent data for both the proton and the
neutron. The analysis uses expansions in complete radial bases to minimize
model dependence and to estimate the uncertainties in radial densities due to
limitation of the range of momentum transfer. We find that the charge
distribution for the proton is significantly broad than its magnetization
density and that the magnetization density is slightly broader for the neutron
than the proton. The neutron charge form factor is consistent with the Galster
parametrization over the available range of Q^2, but relativistic inversion
produces a softer radial density. Discrete ambiguities in the inversion method
are analyzed in detail. The method of Mitra and Kumari ensures compatibility
with pQCD and is most useful for extrapolating form factors to large Q^2.Comment: To appear in Phys. Rev. C. Two new figures and accompanying text have
been added and several discussions have been clarified with no significant
changes to the conclusions. Now contains 47 pages including 21 figures and 2
table
Particle creation, classicality and related issues in quantum field theory: I. Formalism and toy models
The quantum theory of a harmonic oscillator with a time dependent frequency
arises in several important physical problems, especially in the study of
quantum field theory in an external background. While the mathematics of this
system is straightforward, several conceptual issues arise in such a study. We
present a general formalism to address some of the conceptual issues like the
emergence of classicality, definition of particle content, back reaction etc.
In particular, we parametrize the wave function in terms of a complex number
(which we call excitation parameter) and express all physically relevant
quantities in terms it. Many of the notions -- like those of particle number
density, effective Lagrangian etc., which are usually defined using asymptotic
in-out states -- are generalized as time-dependent concepts and we show that
these generalized definitions lead to useful and reasonable results. Having
developed the general formalism we apply it to several examples. Exact analytic
expressions are found for a particular toy model and approximate analytic
solutions are obtained in the extreme cases of adiabatic and highly
non-adiabatic evolution. We then work out the exact results numerically for a
variety of models and compare them with the analytic results and
approximations. The formalism is useful in addressing the question of emergence
of classicality of the quantum state, its relation to particle production and
to clarify several conceptual issues related to this. In Paper II
(arXiv:0708.1237), which is a sequel to this, the formalism will be applied to
analyze the corresponding issues in the context of quantum field theory in
background cosmological models and electric fields.Comment: RevTeX 4; 32 pages; 28 figures; first of a series of two papers, the
second being arXiv:0708.1237 [gr-qc]; high resolution figures available from
the authors on reques
String-localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with
irreducible representations of the Poincar\'e group and localized in
semi-infinite strings extending to spacelike infinity. Among these are fields
that generate the irreducible representations of mass zero and infinite spin
that are known to be incompatible with point-like localized fields. For the
massive representation and the massless representations of finite helicity, all
string-localized free fields can be written as an integral, along the string,
of point-localized tensor or spinor fields. As a special case we discuss the
string-localized vector fields associated with the point-like electromagnetic
field and their relation to the axial gauge condition in the usual setting.Comment: minor correction
Inflation, cold dark matter, and the central density problem
A problem with high central densities in dark halos has arisen in the context
of LCDM cosmologies with scale-invariant initial power spectra. Although n=1 is
often justified by appealing to the inflation scenario, inflationary models
with mild deviations from scale-invariance are not uncommon and models with
significant running of the spectral index are plausible. Even mild deviations
from scale-invariance can be important because halo collapse times and
densities depend on the relative amount of small-scale power. We choose several
popular models of inflation and work out the ramifications for galaxy central
densities. For each model, we calculate its COBE-normalized power spectrum and
deduce the implied halo densities using a semi-analytic method calibrated
against N-body simulations. We compare our predictions to a sample of dark
matter-dominated galaxies using a non-parametric measure of the density. While
standard n=1, LCDM halos are overdense by a factor of 6, several of our example
inflation+CDM models predict halo densities well within the range preferred by
observations. We also show how the presence of massive (0.5 eV) neutrinos may
help to alleviate the central density problem even with n=1. We conclude that
galaxy central densities may not be as problematic for the CDM paradigm as is
sometimes assumed: rather than telling us something about the nature of the
dark matter, galaxy rotation curves may be telling us something about inflation
and/or neutrinos. An important test of this idea will be an eventual consensus
on the value of sigma_8, the rms overdensity on the scale 8 h^-1 Mpc. Our
successful models have values of sigma_8 approximately 0.75, which is within
the range of recent determinations. Finally, models with n>1 (or sigma_8 > 1)
are highly disfavored.Comment: 13 pages, 6 figures. Minor changes made to reflect referee's
Comments, error in Eq. (18) corrected, references updated and corrected,
conclusions unchanged. Version accepted for publication in Phys. Rev. D,
scheduled for 15 August 200
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