Automated derivation of stellar atmospheric parameters and chemical abundances: the MATISSE algorithm

We present an automated procedure for the derivation of atmospheric parameters (Teff, log g, [M/H]) and individual chemical abundances from stellar spectra. The MATrix Inversion for Spectral SythEsis (MATISSE) algorithm determines a basis, B_\theta(\lambda), allowing to derive a particular stellar parameter \theta by projection of an observed spectrum. The B_\theta(\lambda) function is determined from an optimal linear combination of theoretical spectra and it relates, in a quantitative way, the variations in the spectrum flux with variations in \theta. An application of this method to the GAIA/RVS spectral range is described, together with its performances for different types of stars of various metallicities. Blind tests with synthetic spectra of randomly selected parameters and observed input spectra are also presented. The method gives rapid, accurate and stable results and it can be efficiently applied to the study of stellar populations through the analysis of large spectral data sets, including moderate to low signal to noise spectra

A Theory of the Pseudogap State of the Cuprates

The phase diagram for a general model for Cuprates is derived in a mean-field approximation. A phase violating time-reversal without breaking translational symmetry is possible when both the ionic interactions and the local repulsions are large compared to the energy difference between the Cu and O single-particle levels. It ends at a quantum critical point as the hole or electron doping is increased. Such a phase is necessarily accompanied by singular forward scattering such that, in the stable phase, the density of states at the chemical potential, projected to a particular point group symmetry of the lattice is zero producing thereby an anisotropic gap in the single-particle spectrum. It is suggested that this phase occupies the "pseudogap" region of the phase diagram of the cuprates. The temperature dependence of the single-particle spectra, the density of states, the specific heat and the magnetic susceptibility are calculated with rather remarkable correspondence with the experimental results. The importance of further direct experimental verification of such a phase in resolving the principal issues in the theory of the Cuprate phenomena is pointed out. To this end, some predictions are provided.Comment: 41 pages, 8 figure

Theory of Superconductivity in the Cuprates

The quantum critical fluctuations of the time-reversal breaking order parameter which is observed in the pseudogap regime of the Cuprates are shown to couple to the lattice equivalent of the local angular momentum of the fermions. Such a coupling favors scattering of fermions through angles close to $\pm \pi/2$ which is unambiguously shown to promote d-wave pairing. The right order of magnitude of both $T_c$ and the normalized zero temperature gap $\Delta/T_c$ are calculated using the same fluctuations which give the temperature, frequency and momentum dependence of the the anomalous normal state properties for dopings near the quantum-critical value and with two parameters extracted from fit to such experiments.Comment: Accepted for publication in PRB with the title "Theory of the coupling of quantum-critical fluctuations to fermions and d-wave superconductivity in the cuprates

The Multivalued Free-Field Maps of Liouville and Toda Gravities

Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical transformations between interacting and free fields using the technique of intertwining operators, giving explicit constructions for the wavefunctions and showing that they are invariant under the corresponding Weyl groups. These explicit constructions also permit a detailed analysis of the operator-state maps and of the nature of the Seiberg bounds.Comment: 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging to permit Postscript generation, no changes to pape

Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.Comment: 10 pages, 1 figure, submitted to Eur. Phys. J.

Processing of multispectral thermal IR data for geologic applications

Multispectral thermal IR data were acquired with a 24-channel scanner flown in an aircraft over the E. Tintic Utah mining district. These digital image data required extensive computer processing in order to put the information into a format useful for a geologic photointerpreter. Simple enhancement procedures were not sufficient to reveal the total information content because the data were highly correlated in all channels. The data were shown to be dominated by temperature variations across the scene, while the much more subtle spectral variations between the different rock types were of interest. The image processing techniques employed to analyze these data are described

Cooling Rates for Relativistic Electrons Undergoing Compton Scattering in Strong Magnetic Fields

For inner magnetospheric models of hard X-ray and gamma-ray emission in high-field pulsars and magnetars, resonant Compton upscattering is anticipated to be the most efficient process for generating continuum radiation. This is due in part to the proximity of a hot soft photon bath from the stellar surface to putative radiation dissipation regions in the inner magnetosphere. Moreover, because the scattering process becomes resonant at the cyclotron frequency, the effective cross section exceeds the classical Thomson value by over two orders of magnitude, thereby enhancing the efficiency of continuum production and the cooling of relativistic electrons. This paper presents computations of the electron cooling rates for this process, which are needed for resonant Compton models of non-thermal radiation from such highly-magnetized pulsars. The computed rates extend previous calculations of magnetic Thomson cooling to the domain of relativistic quantum effects, sampled near and above the quantum critical magnetic field of 44.13 TeraGauss. This is the first exposition of fully relativistic, quantum magnetic Compton cooling rates for electrons, and it employs both the traditional Johnson and Lippman cross section, and a newer Sokolov and Ternov (ST) formulation of Compton scattering in strong magnetic fields. Such ST formalism is formally correct for treating spin-dependent effects that are important in the cyclotron resonance, and has not been addressed before in the context of cooling by Compton scattering. The QED effects are observed to profoundly lower the rates below extrapolations of the familiar magnetic Thomson results, as expected, when recoil and Klein-Nishina reductions become important.Comment: 33 pages, 11 figures, accepted for publication in The Astrophysical Journa

The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free single and double layer equations exhibit an infinity of spurious solutions and how these can be eliminated at the expense of dealing with (hyper-)singular operators. The high efficiency of the method is demonstrated by numerical calculations in the extreme semiclassical regime.Comment: 28 pages, 12 figure