11,595 research outputs found
The frequency map for billiards inside ellipsoids
The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely
integrable. Its phase space is a symplectic manifold of dimension , which
is mostly foliated with Liouville tori of dimension . The motion on each
Liouville torus becomes just a parallel translation with some frequency
that varies with the torus. Besides, any billiard trajectory inside
is tangent to caustics , so the
caustic parameters are integrals of the
billiard map. The frequency map is a key tool to
understand the structure of periodic billiard trajectories. In principle, it is
well-defined only for nonsingular values of the caustic parameters. We present
four conjectures, fully supported by numerical experiments. The last one gives
rise to some lower bounds on the periods. These bounds only depend on the type
of the caustics. We describe the geometric meaning, domain, and range of
. The map can be continuously extended to singular values of
the caustic parameters, although it becomes "exponentially sharp" at some of
them. Finally, we study triaxial ellipsoids of \Rset^3. We compute
numerically the bifurcation curves in the parameter space on which the
Liouville tori with a fixed frequency disappear. We determine which ellipsoids
have more periodic trajectories. We check that the previous lower bounds on the
periods are optimal, by displaying periodic trajectories with periods four,
five, and six whose caustics have the right types. We also give some new
insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure
On the Equivalence of Three-Particle Scattering Formalisms
In recent years, different on-shell scattering
formalisms have been proposed to be applied to both lattice QCD and infinite
volume scattering processes. We prove that the formulation in the infinite
volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and
subsequently Brice\~no, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can
be recovered from the -matrix representation, derived on the basis of
-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177
(2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore,
both formalisms in the infinite volume are equivalent and the physical content
is identical. Additionally, the Faddeev equations are recovered in the
non-relativistic limit of both representations.Comment: 13 pages, 5 figure
Hints on the quadrupole deformation of the (1232)
The E2/M1 ratio (EMR) of the (1232) is extracted from the world data
in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This
quantity has been derived within a crossing symmetric, gauge invariant, and
chiral symmetric Lagrangian model which also contains a consistent modern
treatment of the (1232) resonance. The \textit{bare} s-channel
(1232) contribution is well isolated and Final State Interactions (FSI)
are effectively taken into account fulfilling Watson's theorem. The obtained
EMR value, EMR%, is in good agreement with the latest lattice
QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with
results of current quark model calculations.Comment: Enlarged conclusions and explanations on the E2/M1 ratio. Figure 3
improved. References updated. 5 pages. 3 figures. 2 tables. Accepted for
publication in Physical Review
On the and Photoproduction Beam Asymmetry at High Energies
We show that, in the Regge limit, beam asymmetries in and
photoproduction are sensitive to hidden strangeness components. Under
reasonable assumptions about the couplings we estimate the contribution of the
Regge pole, which is expected to be the dominant hidden strangeness
contribution. The ratio of the asymmetries in and production is
estimated to be close to unity in the forward region at the photon energy ~GeV, relevant for the upcoming
measurements at Jefferson Lab.Comment: 9 pages, 4 figure
Chemical (in)homogeneity and atomic diffusion in the open cluster M67
Context. The benchmark open cluster M67 is known to have solar metallicity
and similar age as the Sun. It thus provides us a great opportunity to study
the properties of solar twins, as well as the evolution of Sun-like stars.
Aims. Previous spectroscopic studies reported to detect possible subtle changes
in stellar surface abundances throughout the stellar evolutionary phase, namely
the effect of atomic diffusion, in M67. In this study we attempt to confirm and
quantify more precisely the effect of atomic diffusion, as well as to explore
the level of chemical (in)homogeneity in M67. Methods. We presented a strictly
line-by-line differential chemical abundance analysis of two groups of stars in
M67: three turn-off stars and three sub-giants. Stellar atmospheric parameters
and elemental abundances were obtained with very high precision using the
Keck/HIRES spectra. Results. The sub-giants in our sample show negligible
abundance variations ( 0.02 dex), which implies that M67 was born
chemically homogeneous. We note there is a significant abundance difference
( 0.1 - 0.2 dex) between sub-giants and turn-off stars, which can be
interpreted as the signature of atomic diffusion. Qualitatively stellar models
with diffusion agree with the observed abundance results. Some turn-off stars
do not follow the general pattern, which suggests that in some cases diffusion
can be inhibited, or they might suffered some sort of mixing event related to
planets. Conclusions. Our results pose additional challenges for chemical
tagging when using turn-off stars. In particular, the effects of atomic
diffusion, which could be as large as 0.1 - 0.2 dex, must be taken into account
in order for chemical tagging to be successfully applied.Comment: 19 pages, 21 figures; submitted to A&A on February, 2019, accepted
for publication in A&A on June, 201
Searching for galactic sources in the Swift GRB catalog
Since the early 1990s Gamma Ray Bursts have been accepted to be of
extra-galactic origin due to the isotropic distribution observed by BATSE and
the redshifts observed via absorption line spectroscopy. Nevertheless, upon
further examination at least one case turned out to be of galactic origin. This
particular event presented a Fast Rise, Exponential Decay (FRED) structure
which leads us to believe that other FRED sources might also be Galactic. This
study was set out to estimate the most probable degree of contamination by
galactic sources that certain samples of FREDs have. In order to quantify the
degree of anisotropy the average dipolar and quadripolar moments of each sample
of GRBs with respect to the galactic plane were calculated. This was then
compared to the probability distribution of simulated samples comprised of a
combination of isotropically generated sources and galactic sources. We observe
that the dipolar and quadripolar moments of the selected subsamples of FREDs
are found more than two standard deviations outside those of random
isotropically generated samples.The most probable degree of contamination by
galactic sources for the FRED GRBs of the Swift catalog detected until February
2011 that do not have a known redshift is about 21 out of 77 sources which is
roughly equal to 27%. Furthermore we observe, that by removing from this sample
those bursts that may have any type of indirect redshift indicator and multiple
peaks gives the most probable contamination increases up to 34% (17 out of 49
sources). It is probable that a high degree of contamination by galactic
sources occurs among the single peak FREDs observed by Swift.Comment: Published to A&A, 4 pages, 5 figures, this arXiv version includes
appended table with all the bursts considered in this stud
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