Revisiting the optical PTPT-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.Comment: 25 pages, 12 figure

The Site-Diluted Ising Model in Four Dimension

In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.Comment: 15 pages, 5 ps figures. Accepted for publication in Phys. Rev.

Rings and arcs around evolved stars. II. The Carbon Star AFGL 3068 and the Planetary Nebulae NGC 6543, NGC 7009 and NGC 7027

We present a detailed comparative study of the arcs and fragmented ring-like features in the haloes of the planetary nebulae (PNe) NGC 6543, NGC 7009, and NGC 7027 and the spiral pattern around the carbon star AFGL 3068 using high-quality multi-epoch HST images. This comparison allows us to investigate the connection and possible evolution between the regular patterns surrounding AGB stars and the irregular concentric patterns around PNe. The radial proper motion of these features, ~15 km/s, are found to be consistent with the AGB wind and their linear sizes and inter-lapse times (500-1900 yr) also agree with those found around AGB stars, suggesting a common origin. We find evidence using radiative-hydrodynamic simulations that regular patterns produced at the end of the AGB phase become highly distorted by their interactions with the expanding PN and the anisotropic illumination and ionization patterns caused by shadow instabilities. These processes will disrupt the regular (mostly spiral) patterns around AGB stars, plausibly becoming the arcs and fragmented rings observed in the haloes of PNe.Comment: 13 pages, 9 figures, accepted for publication in MNRA

Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_\chi=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.Comment: 11 pages, 11 figures, 14 tables. New analysis (scaling corrections in the g2=0 scenario) and new numerical simulations. Title and conclusions chang

Group Approach to the Quantization of the P\"oschl-Teller dynamics

The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is found in the enveloping algebra of this basic symmetry group. The present algorithm provides a physical realization of the non-unitary, finite-dimensional, irreducible representations of the $SL(2,R)$ group. The non-unitarity manifests itself in that only half of the states are normalizable, in contrast with the representations of SU(2) where all the states are physical.Comment: 17 pages, LaTe

A Chandra Study of the Effects of a Major Merger on the Structure of Abell 2319

We present an analysis of a Chandra observation of the massive, nearby galaxy cluster Abell 2319. A sharp surface brightness discontinuity--suggested by previous, lower angular resolution X-ray imaging--is clearly visible in the ACIS image. This roughly 300kpc feature suggests that a major merger is taking place with a significant velocity component perpendicular to the line of sight. The cluster emission-weighted mean temperature is 11.8+/-0.6kev, somewhat higher than previous temperature measurements. The Chandra temperature map of A2319 reveals substructure resembling that anticipated based on hydrodynamic simulations of cluster mergers. The merger feature shows a pressure change across the surface brightness discontinuity by a factor of <=2.5. The higher density side of the front has a lower temperature, suggesting the presence of a cold front similar to those in many other merging clusters. The velocity of the front is roughly sonic. We compare bulk properties of the ICM and galaxies in A2319 to the same properties in a large sample of clusters as a way of gauging the effects of the major merger. Interestingly, by comparing A2319 to a sample of 44 clusters studied with the ROSAT PSPC we find that the X-ray luminosity, isophotal size, and ICM mass are consistent with the expected values for a cluster of its temperature; in addition, the K-band galaxy light is consistent with the light--temperature scaling relation derived from a sample of about 100 clusters studied with 2MASS. Together, these results indicate either that the merger in A2319 has not been effective at altering the bulk properties of the cluster, or that there are large but correlated displacements in these quantities.Comment: 11 pages, 8 figures, ApJ Submitte

Detection of new eruptions in the Magellanic Clouds LBVs R 40 and R 110

We performed a spectroscopic and photometric analysis to study new eruptions in two luminous blue variables (LBVs) in the Magellanic Clouds. We detected a strong new eruption in the LBV R40 that reached $V \sim 9.2$ in 2016, which is around $1.3$ mag brighter than the minimum registered in 1985. During this new eruption, the star changed from an A-type to a late F-type spectrum. Based on photometric and spectroscopic empirical calibrations and synthetic spectral modeling, we determine that R\,40 reached $T_{\mathrm{eff}} = 5800-6300$~K during this new eruption. This object is thereby probably one of the coolest identified LBVs. We could also identify an enrichment of nitrogen and r- and s-process elements. We detected a weak eruption in the LBV R 110 with a maximum of $V \sim 9.9$ mag in 2011, that is, around $1.0$ mag brighter than in the quiescent phase. On the other hand, this new eruption is about $0.2$ mag fainter than the first eruption detected in 1990, but the temperature did not decrease below 8500 K. Spitzer spectra show indications of cool dust in the circumstellar environment of both stars, but no hot or warm dust was present, except by the probable presence of PAHs in R\,110. We also discuss a possible post-red supergiant nature for both stars

Finite-Difference Equations in Relativistic Quantum Mechanics

Relativistic Quantum Mechanics suffers from structural problems which are traced back to the lack of a position operator $\hat{x}$, satisfying $[\hat{x},\hat{p}]=i\hbar\hat{1}$ with the ordinary momentum operator $\hat{p}$, in the basic symmetry group -- the Poincar\'e group. In this paper we provide a finite-dimensional extension of the Poincar\'e group containing only one more (in 1+1D) generator $\hat{\pi}$, satisfying the commutation relation $[\hat{k},\hat{\pi}]=i\hbar\hat{1}$ with the ordinary boost generator $\hat{k}$. The unitary irreducible representations are calculated and the carrier space proves to be the set of Shapiro's wave functions. The generalized equations of motion constitute a simple example of exactly solvable finite-difference set of equations associated with infinite-order polarization equations.Comment: 10 LaTeX pages, final version, enlarged (2 more pages

Non-central panorama indoor dataset

Omnidirectional images are one of the main sources of information for learning-based scene understanding algorithms. However, annotated datasets of omnidirectional images cannot keep the pace of these learning-based algorithms development. Among the different panoramas and in contrast to standard central ones, non-central panoramas provide geometrical information in the distortion of the image from which we can retrieve 3D information of the environment. However, due to the lack of commercial non-central devices, up until now there was no dataset of these kind of panoramas. In this data paper, we present the first dataset of non-central panoramas for indoor scene understanding. The dataset is composed of 2574 RGB non-central panoramas taken in around 650 different rooms. Each panorama has associated a depth map and annotations to obtain the layout of the room from the image as a structural edge map, list of corners in the image, the 3D corners of the room and the camera pose. The images are taken from photorealistic virtual environments and pixel-wise automatically annotated