5,377 research outputs found
Generalised model-independent characterisation of strong gravitational lenses II: Transformation matrix between multiple images
(shortened) We determine the transformation matrix T that maps multiple
images with resolved features onto one another and that is based on a
Taylor-expanded lensing potential close to a point on the critical curve within
our model-independent lens characterisation approach. From T, the same
information about the critical curve at fold and cusp points is derived as
determined by the quadrupole moment of the individual images as observables. In
addition, we read off the relative parities between the images, so that the
parity of all images is determined, when one is known. We compare all
retrievable ratios of potential derivatives to the actual ones and to those
obtained by using the quadrupole moment as observable for two and three image
configurations generated by a galaxy-cluster scale singular isothermal ellipse.
We conclude that using the quadrupole moments as observables, the properties of
the critical curve at the cusp points are retrieved to higher accuracy, at the
fold points to lower accuracy, and the ratios of second order potential
derivatives to comparable accuracy. We show that the approach using ratios of
convergences and reduced shear is equivalent to ours close to the critical
curve but yields more accurate results and is more robust because it does not
require a special coordinate system like the approach using potential
derivatives. T is determined by mapping manually assigned reference points in
the images onto each other. If the assignment of reference points is subject to
measurement uncertainties under noise, we find that the confidence intervals of
the lens parameters can be as large as the values, when the uncertainties are
larger than one pixel. Observed multiple images with resolved features are more
extended than unresolved ones, so that higher order moments should be taken
into account to improve the reconstruction.Comment: 13 pages, 12 figures, submitted to Astronomy & Astrophysics, comments
welcom
Model-independent and model-based local lensing properties of CL0024+1654 from multiply-imaged galaxies
We investigate to which precision local magnification ratios, ,
ratios of convergences, , and reduced shears, , can be
determined model-independently for the five resolved multiple images of the
source at in CL0024. We also determine if a comparison to
the respective results obtained by the parametric modelling program Lenstool
and by the non-parametric modelling program Grale can detect biases in the lens
models. For these model-based approaches we additionally analyse the influence
of the number and location of the constraints from multiple images on the local
lens properties determined at the positions of the five multiple images of the
source at . All approaches show high agreement on the local
values of , , and . We find that Lenstool obtains the
tightest confidence bounds even for convergences around one using constraints
from six multiple image systems, while the best Grale model is generated only
using constraints from all multiple images with resolved brightness features
and adding limited small-scale mass corrections. Yet, confidence bounds as
large as the values themselves can occur for convergences close to one in all
approaches. Our results are in agreement with previous findings, supporting the
light-traces-mass assumption and the merger hypothesis for CL0024. Comparing
the three different approaches allows to detect modelling biases. Given that
the lens properties remain approximately constant over the extension of the
image areas covered by the resolvable brightness features, the
model-independent approach determines the local lens properties to a comparable
precision but within less than a second. (shortened)Comment: 22 pages, published in A&A 612 A17, comments welcom
Excited states of neutral donor bound excitons in GaN
We investigate the excited states of a neutral donor bound exciton (D0X) in bulk GaN by means of high-resolution, polychromatic photoluminescence excitation (PLE) spectroscopy. The optically most prominent donor in our sample is silicon accompanied by only a minor contribution of oxygen—the key for an unambiguous assignment of excited states. Consequently, we can observe a multitude of Si0X-related excitation channels with linewidths down to 200 μeV. Two groups of excitation channels are identified, belonging either to rotational-vibrational or electronic excited states of the hole in the Si0X complex. Such identification is achieved by modeling the excited states based on the equations of motion for a Kratzer potential, taking into account the particularly large anisotropy of effective hole masses in GaN. Furthermore, several ground- and excited states of the exciton-polaritons and the dominant bound exciton are observed in the photoluminescence (PL) and PLE spectra, facilitating an estimate of the associated complex binding energies. Our data clearly show that great care must be taken if only PL spectra of D0X centers in GaN are analyzed. Every PL feature we observe at higher emission energies with regard to the Si0X ground state corresponds to an excited state. Hence, any unambiguous peak identification renders PLE spectra highly valuable, as important spectral features are obscured in common PL spectra. Here, GaN represents a particular case among the wide-bandgap, wurtzite semiconductors, as comparably low localization energies for common D0X centers are usually paired with large emission linewidths and the prominent optical signature of exciton-polaritons, making the sole analysis of PL spectra a challenging task.EC/H2020/749565/EU/Heat Transport and its Effects on the Performance of Nanostructured, Photonic Materials/PhotoHeatEffectDFG, 43659573, SFB 787: Halbleiter - Nanophotonik: Materialien, Modelle, Bauelement
Strategic investment and learning with private information
We study a two-player game of strategic experimentation in which agents choose the timing of investments which yield uncertain returns over time. Agents learn about future returns through privately observed signals, others’ investment decisions and from public experimentation outcomes when returns are realized. We characterize symmetric equilibria, and we relate the extent of strategic delay of investments in equilibrium to the primitives of the information structure. Agents invest without delay when the most optimistic intermediate belief exceeds a threshold. Otherwise, delay in investments induces a negative learning feed-back which may either escalate or dampen beliefs and investment choices. We highlight how private information in strategic experimentation can increase ex ante welfare because of strategic uncertainty and due to an «encouragement effect of private information»
Bell correlations in a many-body system with finite statistics
A recent experiment reported the first violation of a Bell correlation
witness in a many-body system [Science 352, 441 (2016)]. Following discussions
in this paper, we address here the question of the statistics required to
witness Bell correlated states, i.e. states violating a Bell inequality, in
such experiments. We start by deriving multipartite Bell inequalities involving
an arbitrary number of measurement settings, two outcomes per party and one-
and two-body correlators only. Based on these inequalities, we then build up
improved witnesses able to detect Bell-correlated states in many-body systems
using two collective measurements only. These witnesses can potentially detect
Bell correlations in states with an arbitrarily low amount of spin squeezing.
We then establish an upper bound on the statistics needed to convincingly
conclude that a measured state is Bell-correlated.Comment: 5+12 pages, 3+4 figure
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