On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Introduction to the functional RG and applications to gauge theories

These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow equation for the effective average action. The second lecture is devoted to a discussion of flow equations and symmetries in general, and flow equations and gauge symmetries in particular. The third lecture deals with the flow equation in the background formalism which is particularly convenient for analytical computations of truncated flows. The fourth lecture concentrates on the transition from microscopic to macroscopic degrees of freedom; even though this is discussed here in the language and the context of QCD, the developed formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Ital

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss

A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results

Transactional paths between children and parents in pediatric asthma: Associations between family relationships and adaptation

Introduction. The particular challenges posed by pediatric asthma may have a negative impact on the adaptation of children and their parents. From a transactional approach it is important to examine how reciprocal links between children and parents contribute to explain their adaptation and under which conditions these associations occur. This cross-sectional study aimed at examining the direct and indirect links between children’s and parents’ perceptions of family relationships and adaptation, separately (within-subjects) and across participants (cross-lagged effects), and the role of asthma severity in moderating these associations. Method. The sample comprised 257 children with asthma, aged between 8 and 18 years-old, and one of their parents. Both family members completed self-reported questionnaires on family relationships (cohesion and expressiveness) and adaptation indicators (quality of life and psychological functioning). Physicians assessed asthma severity. Structural Equation Modeling was used to test within-subjects and cross-lagged paths between children’s and parents’ family relationships and adaptation. Results. The model explained 47% of children’s and 30% of parents’ adaptation: family relationships were positively associated with adaptation, directly for children and parents, and indirectly across family members. Asthma severity moderated the association between family relationships and health-related quality of life for children: stronger associations were observed in the presence of persistent asthma. Conclusion. These results highlight the need of including psychological interventions in pediatric healthcare focused on family relationships as potential targets for improving children’s and parents’ quality of life and psychological functioning, and identified the children with persistent asthma as a group that would most benefit from family-based interventions.This study was supported by the R&D Unit Institute of Cognitive Psychology, Vocational and Social Development of the University of Coimbra (PEst-OE/PSI/UI0192/2011) and by the Portuguese Foundation for Science and Technology (PhD Grant SFRH/BD/69885/2010)

Nonlinear Beam Propagation in a Class of Complex Non-PT -Symmetric Potentials

The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schr\"odinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it might be the case in realistic applications. We utilize two parameters: the first one breaks PT-symmetry but retains a proportionality between the imaginary and the derivative of the real part of the potential; the second one, detunes from this latter proportionality. It is shown that the departure of the potential from the PT -symmetric form does not allow for the numerical identification of exact stationary solutions. Nevertheless, it is of crucial importance to consider the dynamical evolution of initial beam profiles. In that light, we define a suitable notion of optimization and find that even for non PT-symmetric cases, the beam dynamics, both in 1D and 2D -although prone to weak growth or decay- suggests that the optimized profiles do not change significantly under propagation for specific parameter regimes

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

Physics of Neutron Star Crusts

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.Comment: 182 pages, published version available at <http://www.livingreviews.org/lrr-2008-10