Invariant Manifolds and Collective Coordinates

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st

Measurement of Spinal Sagittal Curvatures using the Laser Triangulation Method

The purpose of the first part of the study was to establish the variability of repeated measurements in different measuring conditions. In the second part, we performed in a large number of patients, a measurement of thoracic kyphosis and lumbar lordosis and compared them to age, gender, and level of nourishment. In the first part, measurements were performed on a plastic model of the back of a patient with a rigid and a normal spine. In the second part, 250 patients participated in the study (126 men and 124 women). For measuring spinal curvatures we used an apparatus for laser triangulation constructed at the Faculty of Mechanical Engineering, University of Ljubljana. A comparison of 30 repeated measurements was shown as the average value±2 SD which included 95% of the results. Thirty repeated readings of one 3D measurement: thoracic kyphosis 41.2°±0.6°, lumbar lordosis 4.4°±1.2°; 30 measurements on a plastic model: thoracic kyphosis 36.8°±1.2°, lumbar lordosis 30.9°±2.0°; 30 measurements on a patient with a rigid spine: thoracic kyphosis 41.5°±2.4°, lumbar lordosis 4.0°±1.8°; 30 measurements on a patient with a normal spine: thoracic kyphosis 48.8°±7.4°, lumbar lordosis 21.1°±4.4°. The average size of thoracic kyphosis in 250 patients was 46.8° (SD 10.1°) and lumbar lordosis 31.7° (SD 12.5°). The angle size was statistically significantly correlated to gender (increased thoracic kyphosis and lumbar lordosis in women) and body mass index (increased thoracic kyphosis and lumbar lordosis in more nourished patients). Age was not significantly correlated to the observed angles. During measurements of the spinal angles it was important to pay attention to relaxation and the patient’s position as well as to perform more measurements providing the average value. The age and the level of nourishment influence the size of the sagittal spinal angles. In the observed sample the effect of age was not confirmed

Signatures of the disk-jet coupling in the Broad-line Radio Quasar 4C+74.26

Here we explore the disk-jet connection in the broad-line radio quasar 4C+74.26, utilizing the results of the multiwavelength monitoring of the source. The target is unique in that its radiative output at radio wavelengths is dominated by a moderately-beamed nuclear jet, at optical frequencies by the accretion disk, and in the hard X-ray range by the disk corona. Our analysis reveals a correlation (local and global significance of 96\% and 98\%, respectively) between the optical and radio bands, with the disk lagging behind the jet by $250 \pm 42$ days. We discuss the possible explanation for this, speculating that the observed disk and the jet flux changes are generated by magnetic fluctuations originating within the innermost parts of a truncated disk, and that the lag is related to a delayed radiative response of the disk when compared with the propagation timescale of magnetic perturbations along relativistic outflow. This scenario is supported by the re-analysis of the NuSTAR data, modelled in terms of a relativistic reflection from the disk illuminated by the coronal emission, which returns the inner disk radius $R_{\rm in}/R_{\rm ISCO} =35^{+40}_{-16}$. We discuss the global energetics in the system, arguing that while the accretion proceeds at the Eddington rate, with the accretion-related bolometric luminosity $L_{\rm bol} \sim 9 \times 10^{46}$ erg s$^{-1}$ $\sim 0.2 L_{\rm Edd}$, the jet total kinetic energy $L_\textrm{j} \sim 4 \times 10^{44}$ erg s$^{-1}$, inferred from the dynamical modelling of the giant radio lobes in the source, constitutes only a small fraction of the available accretion power.Comment: 9 pages and 6 figures, ApJ accepte

Precursor flares in OJ 287

We have studied three most recent precursor flares in the light curve of the blazar OJ 287 while invoking the presence of a precessing binary black hole in the system to explain the nature of these flares. Precursor flare timings from the historical light curves are compared with theoretical predictions from our model that incorporate effects of an accretion disk and post-Newtonian description for the binary black hole orbit. We find that the precursor flares coincide with the secondary black hole descending towards the accretion disk of the primary black hole from the observed side, with a mean z-component of approximately z_c = 4000 AU. We use this model of precursor flares to predict that precursor flare of similar nature should happen around 2020.96 before the next major outburst in 2022.Comment: to appear in the Astrophysical Journa

Dynamics of open quantum systems

The coupling between the states of a system and the continuum into which it is embedded, induces correlations that are especially large in the short time scale. These correlations cannot be calculated by using a statistical or perturbational approach. They are, however, involved in an approach describing structure and reaction aspects in a unified manner. Such a model is the SMEC (shell model embedded in the continuum). Some characteristic results obtained from SMEC as well as some aspects of the correlations induced by the coupling to the continuum are discussed.Comment: 16 pages, 5 figure

Density-matrix formalism with three-body ground-state correlations

A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition

Absolute properties of the binary system BB Pegasi

We present a ground based photometry of the low-temperature contact binary BB Peg. We collected all times of mid-eclipses available in literature and combined them with those obtained in this study. Analyses of the data indicate a period increase of 3.0(1) x 10^{-8} days/yr. This period increase of BB Peg can be interpreted in terms of the mass transfer 2.4 x 10^{-8} Ms yr^{-1} from the less massive to the more massive component. The physical parameters have been determined as Mc = 1.42 Ms, Mh = 0.53 Ms, Rc = 1.29 Rs, Rh = 0.83 Rs, Lc = 1.86 Ls, and Lh = 0.94 Ls through simultaneous solution of light and of the radial velocity curves. The orbital parameters of the third body, that orbits the contact system in an eccentric orbit, were obtained from the period variation analysis. The system is compared to the similar binaries in the Hertzsprung-Russell and Mass-Radius diagram.Comment: 17 pages, 3 figures, accepted for Astronomical Journa

Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on statistics of $Z_i$ for systems with broken time-reversal invariance and verify that it allows to reproduce statistical characteristics of Wigner time delays known from independent calculations. We analyze the ensuing two-point statistical measures as e.g. spectral form factor and the number variance. In addition we find the density of complex eigenvalues of real asymmetric matrices generalizing the recent result by Efetov\cite{Efnh}.Comment: 4 page