Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Diquark and Pion Condensation in Random Matrix Models for two-color QCD

We introduce a random matrix model with the symmetries of QCD with two colors at nonzero isospin and baryon chemical potentials and temperature. We analyze its phase diagram and find phases with condensation of pion and diquark states in addition to the phases with spontaneously broken chiral symmetries. In the limit of small chemical potentials and quark masses, we reproduce the mean field results obtained from chiral Lagrangians. As in the case of QCD with three colors, the presence of two chemical potentials breaks the flavor symmetry and leads to phases that are characterized by different behaviors of the chiral condensates for each flavor. In particular, the phase diagram we obtain is similar to QCD with three colors and three flavors of quarks of equal masses at zero baryon chemical potential and nonzero isospin and strange chemical potentials. A tricritical point of the superfluid transitions found in lattice calculations and from an analysis in terms of chiral Lagrangians does not appear in the random matrix model. Remarkably, at fixed isospin chemical potential, for the regions outside of the superfluid phases, the phase diagram in the temperature - baryon chemical potential plane for two colors and three colors are qualitatively the same.Comment: 19 pages, 7 figures, RevTeX

Gravity from Spinors

We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of Einstein's equations due to the lack of local Lorentz-symmetry. We explore the generalized gravity with global instead of local Lorentz symmetry in first order of a systematic derivative expansion. At this level diffeomorphisms and global Lorentz symmetry allow for two new invariants in the gravitational effective action. The one which arises in the one loop approximation to spinor gravity is consistent with all present tests of general relativity and cosmology. This shows that local Lorentz symmetry is tested only very partially by present observations. In contrast, the second possible new coupling is severely restricted by present solar system observations.Comment: New material on absence of observational tests of local Lorentz invariance, 21 pages, to appear in Phys.Rev.

A 1.3 cm line survey toward IRC +10216

IRC +10216 is the prototypical carbon star exhibiting an extended molecular circumstellar envelope. Its spectral properties are therefore the template for an entire class of objects. The main goal is to systematically study the $\lambda$ $\sim$1.3 cm spectral line characteristics of IRC +10216. We carried out a spectral line survey with the Effelsberg-100 m telescope toward IRC +10216. It covers the frequency range between 17.8 GHz and 26.3 GHz (K-band). In the circumstellar shell of IRC +10216, we find 78 spectral lines, among which 12 remain unidentified. The identified lines are assigned to 18 different molecules and radicals. A total of 23 lines from species known to exist in this envelope are detected for the first time outside the Solar System and there are additional 20 lines first detected in IRC +10216. The potential orgin of "U" lines is also discussed. Assuming local thermodynamic equilibrium (LTE), we then determine rotational temperatures and column densities of 17 detected molecules. Molecular abundances relative to H$_{2}$ are also estimated. A non-LTE analysis of NH$_{3}$ shows that the bulk of its emission arises from the inner envelope with a kinetic temperature of 70$\pm$20 K. Evidence for NH$_{3}$ emitting gas with higher kinetic temperature is also obtained, and potential abundance differences between various $^{13}$C-bearing isotopologues of HC$_{5}$N are evaluated. Overall, the isotopic $^{12}$C/$^{13}$C ratio is estimated to be 49$\pm$9. Finally, a comparison of detected molecules in the $\lambda$ $\sim$1.3 cm range with the dark cloud TMC-1 indicates that silicate-bearing molecules are more predominant in IRC +10216.Comment: 32 pages, 9 figures, Accepted by A&

A 1.3 cm Line Survey toward Orion KL

Orion KL has served as a benchmark for spectral line searches throughout the (sub)millimeter regime. The main goal is to systematically study spectral characteristics of Orion KL in the 1.3 cm band. We carried out a spectral line survey (17.9 GHz to 26.2 GHz) with the Effelsberg-100 m telescope towards Orion KL. We find 261 spectral lines, yielding an average line density of about 32 spectral features per GHz above 3$\sigma$. The identified lines include 164 radio recombination lines (RRLs) and 97 molecular lines. A total of 23 molecular transitions from species known to exist in Orion KL are detected for the first time in the interstellar medium. Non-metastable 15NH3 transitions are detected in Orion KL for the first time. Based on the velocity information of detected lines and the ALMA images, the spatial origins of molecular emission are constrained and discussed. A narrow feature is found in SO2 ($8_{1,7}-7_{2,6}$), possibly suggesting the presence of a maser line. Column densities and fractional abundances relative to H2 are estimated for 12 molecules with LTE methods. Rotational diagrams of non-metastable 14NH3 transitions with J=K+1 to J=K+4 yield different results; metastable 15NH3 is found to have a higher excitation temperature than non-metastable 15NH3, indicating that they may trace different regions. Elemental and isotopic abundance ratios are estimated: 12C/13C=63+-17, 14N/15N=100+-51, D/H=0.0083+-0.0045. The dispersion of the He/H ratios derived from H$\alpha$/He$\alpha$ pairs to H$\delta$/He$\delta$ pairs is very small, which is consistent with theoretical predictions that the departure coefficients bn factors for hydrogen and helium are nearly identical. Based on a non-LTE code neglecting excitation by the infrared radiation field and a likelihood analysis, we find that the denser regions have lower kinetic temperature, which favors an external heating of the Hot Core.Comment: 70 pages, 26 figures, 12 tables, accepted for publication in A&A. Figs. 1, 2, 8, 9 have been downsize

Robust Ferroelectric State in Multiferroic Mn1−x_{1-x}Znx_xWO4_4

We report the remarkably robust ferroelectric state in the multiferroic compound Mn$_{1-x}$Zn$_x$WO$_4$. The substitution of the magnetic Mn$^{2+}$ with nonmagnetic Zn$^{2+}$ reduces the magnetic exchange and provides control of the various magnetic and multiferroic states of MnWO$_4$. Only 5 % of Zn substitution results in a complete suppression of the frustrated collinear (paraelectric) low temperature phase. The helical magnetic and ferroelectric phase develops as the ground state. The multiferroic state is stable up to a high level of substitution of more than 50 %. The magnetic, thermodynamic, and dielectric properties as well as the ferroelectric polarization of single crystals of Mn$_{1-x}$Zn$_x$WO$_4$ are studied for different substitutions up to x=0.5. The magnetic phases have been identified in single crystal neutron scattering experiments. The ferroelectric polarization scales with the neutron intensity of the incommensurate peak of the helical phase.Comment: 6 pages, 8 figure

Harrison transformation of hyperelliptic solutions and charged dust disks

We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail. Analytic expressions for the metric and the multipole moments are obtained. As an example we consider the transformation of a family of counter-rotating dust disks. The resulting solutions can be interpreted as disks with currents and matter with a purely azimuthal pressure or as two streams of freely moving charged particles. We discuss interesting limiting cases as the extreme limit where the charge becomes identical to the mass, and the ultrarelativistic limit where the central redshift diverges.Comment: 20 pages, 9 figure

Batch drying in sintering

An adapted mathematical model of sintering permits analysis of the thermophysical characteristics of batch drying, primarily in the main sintering period. Over the whole length of the sintering machine, most of the bed volume corresponds to equilibrium moisture content, which may be higher or lower than the initial value. The temperature of the gas entering the drying zone is calculated, and its dependence on the parameters of the batch and gas is determined. © 2013 Allerton Press, Inc