4,336 research outputs found
Combinatorics of lattice paths with and without spikes
We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.Comment: Latex. 25 page
Large reduction with the Twisted Eguchi-Kawai model
We examine the breaking of symmetry recently reported for the Twisted
Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose
simple modifications of twist and lattice action that could avoid the problem.
Our results show no sign of symmetry breaking and allow us to obtain values of
the large infinite volume string tension in agreement with extrapolations
from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure
Integrability in Theories with Local U(1) Gauge Symmetry
Using a recently developed method, based on a generalization of the zero
curvature representation of Zakharov and Shabat, we study the integrability
structure in the Abelian Higgs model. It is shown that the model contains
integrable sectors, where integrability is understood as the existence of
infinitely many conserved currents. In particular, a gauge invariant
description of the weak and strong integrable sectors is provided. The
pertinent integrability conditions are given by a U(1) generalization of the
standard strong and weak constraints for models with two dimensional target
space. The Bogomolny sector is discussed, as well, and we find that each
Bogomolny configuration supports infinitely many conserved currents. Finally,
other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.
Adjoint modes as probes of gauge field structure
We show how zero-modes and quasi-zero-modes of the Dirac operator in the
adjoint representation can be used to construct an estimate of the action
density distribution of a pure gauge field theory, which is less sensitive to
the ultraviolet fluctuations of the field. This can be used to trace the
topological structures present in the vacuum. The construction relies on the
special properties satisfied by the supersymmetric zero-modes.Comment: Latex file. 29 pages and 12 figure
VLTI/AMBER spectro-interferometry of the late-type supergiants V766 Cen (=HR 5171 A), sigma Oph, BM Sco, and HD 206859
We add four warmer late-type supergiants to our previous
spectro-interferometric studies of red giants and supergiants.
V766 Cen (=HR 5171 A) is found to be a high-luminosity log(L/L_sun)=5.8+-0.4
source of Teff 4290+-760 K and radius 1490+-540 Rsun located close to both the
Hayashi and Eddington limits; this source is consistent with a 40 Msun
evolutionary track without rotation and current mass 27-36 Msun. It exhibits
NaI in emission arising from a shell of radius 1.5 Rphot and a photocenter
displacement of about 0.1 Rphot. V766 Cen shows strong extended molecular (CO)
layers and a dusty circumstellar background component. This suggest an
optically thick pseudo-photosphere at about 1.5 Rphot at the onset of the wind.
V766 Cen is a red supergiant located close to the Hayashi limit instead of a
yellow hypergiant already evolving back toward warmer Teff as previously
discussed.
The stars sigma Oph, BM Sco, and HD 206859 are found to have lower
luminosities of about log(L/Lsun)=3.4-3.5 and Teff of 3900-5300 K,
corresponding to 5-9 Msun tracks. They do not show extended molecular layers as
observed for higher luminosity red supergiants of our sample. BM Sco shows an
unusually strong contribution by an over-resolved circumstellar dust component.
These stars are more likely high-mass red giants instead of red supergiants.
This leaves us with an unsampled locus in the HR diagram corresponding to
luminosities log(L/Lsun)~3.8-4.8 or masses 10-13 Msun, possibly corresponding
to the mass region where stars explode as type II-P supernovae during the RSG
stage.
Our previously found relation of increasing strength of extended molecular
layers with increasing luminosities is now confirmed to extend to double our
previous luminosities and up to the Eddington limit. This might further point
to steadily increasing radiative winds with increasing luminosity.
[Abridged]Comment: 16 pages, 14 figures, accepted for publication in Astronomy and
Astrophysics (A&A
Wide Localized Solitons in Systems with Time and Space-Modulated Nonlinearities
In this work we apply point canonical transformations to solve some classes
of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess
specific cubic and quintic - time and space dependent - nonlinearities. In this
way we generalize some procedures recently published which resort to an ansatz
to the wavefunction and recover a time and space independent nonlinear equation
which can be solved explicitly. The method applied here allow us to find wide
localized (in space) soliton solutions to the nonautonomous nonlinear
Schr\"{o}dinger equation, which were not presented before. We also generalize
the external potential which traps the system and the nonlinearities terms.Comment: 19 pages, 5 figure
What causes the large extensions of red-supergiant atmospheres? Comparisons of interferometric observations with 1-D hydrostatic, 3-D convection, and 1-D pulsating model atmospheres
We present the atmospheric structure and the fundamental parameters of three
red supergiants, increasing the sample of RSGs observed by near-infrared
spectro-interferometry. Additionally, we test possible mechanisms that may
explain the large observed atmospheric extensions of RSGs.
We carried out spectro-interferometric observations of 3 RSGs in the
near-infrared K-band with the VLTI/AMBER instrument at medium spectral
resolution. To comprehend the extended atmospheres, we compared our
observational results to predictions by available hydrostatic PHOENIX,
available 3-D convection, and new 1-D self-excited pulsation models of RSGs.
Our near-infrared flux spectra are well reproduced by the PHOENIX model
atmospheres. The continuum visibility values are consistent with a
limb-darkened disk as predicted by the PHOENIX models, allowing us to determine
the angular diameter and the fundamental parameters of our sources.
Nonetheless, in the case of V602 Car and HD 95686, the PHOENIX model
visibilities do not predict the large observed extensions of molecular layers,
most remarkably in the CO bands. Likewise, the 3-D convection models and the
1-D pulsation models with typical parameters of RSGs lead to compact
atmospheric structures as well, which are similar to the structure of the
hydrostatic PHOENIX models. They can also not explain the observed decreases in
the visibilities and thus the large atmospheric molecular extensions. The full
sample of our RSGs indicates increasing observed atmospheric extensions with
increasing luminosity and decreasing surface gravity, and no correlation with
effective temperature or variability amplitude, which supports a scenario of
radiative acceleration on Doppler-shifted molecular lines.Comment: Accepted for publication in A&
Vortex solutions in the noncommutative torus
Vortex configurations in the two-dimensional torus are considered in
noncommutative space. We analyze the BPS equations of the Abelian Higgs model.
Numerical solutions are constructed for the self-dual and anti-self dual cases
by extending an algorithm originally developed for ordinary commutative space.
We work within the Fock space approach to noncommutative theories and the
Moyal-Weyl connection is used in the final stage to express the solutions in
configuration space.Comment: 18 pages, 5 figure
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