Adding and multiplying random matrices: a generalization of Voiculescu's formulae

In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large $N$ random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulae to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices.Comment: 11 pages, harvmac. revised x 2: refs and minor comments adde

A Predictive Minimal Model for Neutrino Masses and Mixings

A model is considered in which the scale of the heavy singlet neutrinos is a few orders of magnitude below the grand unification scale and where right-handed vector bosons play still a negligible role. In a basis with diagonal up-quark and Dirac-neutrino mass matrices it is assumed that the heavy neutrino mass matrix has only zero elements in its diagonal, in analogy to the light neutrino mass matrix in the Zee model. Connecting then the remaining matrix elements with the small parameter describing the hierarchy of quark masses and mixings and by assuming commutativity of the charged lepton with the down-quark mass matrix, the calculation of all neutrino properties can be performed in terms of the two mass differences relevant for atmospheric and solar neutrino oscillations. CP-violation is directly related to CP-violation in the quark sector.Comment: revtex, 9 pages, two references added, to be published in Phys. Rev. D presented at Neutrino' 2000, Sudbury, Canad

H-alpha Survey of the Local Volume: Isolated Southern Galaxies

We present our H-alpha observations of 11 isolated southern galaxies: SDIG, PGC 51659, E 222-010, E 272-025, E 137-018, IC 4662, Sag DIG, IC 5052, IC 5152, UGCA 438, and E149-003, with distances from 1 to 7 Mpc. We have determined the total H-alpha fluxes from these galaxies. The star formation rates in these galaxies range from 10^{-1} (IC 4662) to 10^{-4}_{\odot}/yr (SDIG) and the gas depletion time at the observed star formation rates lies within the range from 1/6 to 24 Hubble times H_0^{-1} .Comment: 9 pages, 3 figure

The Origin of Structures in Generalized Gravity

In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we can describe the quantum generation and the classical evolution of both the scalar and tensor structures in a simple and unified manner. An accelerated expansion phase based on the generalized gravity in the early universe drives microscopic quantum fluctuations inside a causal domain to expand into macroscopic ripples in the spacetime metric on scales larger than the local horizon. Following their generation from quantum fluctuations, the ripples in the metric spend a long period outside the causal domain. During this phase their evolution is characterized by their conserved amplitudes. The evolution of these fluctuations may lead to the observed large scale structures of the universe and anisotropies in the cosmic microwave background radiation.Comment: 5 pages, latex, no figur

Complete diagrammatics of the single ring theorem

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio

FUSE observations of the HI interstellar gas of IZw18

We present the analysis of FUSE observations of the metal-deficient dwarf galaxy IZw18. We measured column densities of HI, NI, OI, ArI, SiII, and FeII. The OI/HI ratio (log(OI/HI)=-4.7^{+0.8}_{-0.6}) is consistent with the O/H ratio observed in the HII regions (all uncertainties are 2-sigma). If the oxygen is depleted in the HI region compared to the HII regions, the depletion is at most 0.5dex. This is also consistent with the log(O/H) ratios ~-5 measured with FUSE in the HI regions of other blue compact dwarf galaxies. With log(NI/OI)=-2.4^{+0.6}_{-0.8}, the measured NI/OI ratio is lower than expected for primary nitrogen. The determination of the NII column density is needed to discriminate between a large ionization of NI or a possible nitrogen deficiency. The neutral argon is also apparently underabundant, indicating that ionization into ArII is likely important. The column densities of the other alpha-chain elements SiII and ArI favor the lower edge of the permitted range of OI column density, log(N(OI))~16.3.Comment: Accepted for publication in A&

Dynamical Solutions to the Horizon and Flatness Problems

We discuss in some detail the requirements on an early-Universe model that solves the horizon and flatness problems during the epoch of classical cosmology ($t\ge t_i\gg 10^{-43}\sec$). We show that a dynamical resolution of the horizon problem requires superluminal expansion (or very close to it) and that a truly satisfactory resolution of the flatness problem requires entropy production. This implies that a proposed class of adiabatic models in which the Planck mass varies by many orders of magnitude cannot fully resolve the flatness problem. Furthermore, we show that, subject to minimal assumptions, such models cannot solve the horizon problem either. Because superluminal expansion and entropy production are the two generic features of inflationary models, our results suggest that inflation, or something very similar, may be the only dynamical solution to the horizon and flatness problems.Comment: 17 page

New Cosmic Accelerating Scenario without Dark Energy

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model ($\Lambda$CDM) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes sub-dominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard $\Lambda$CDM model, however, there is no dark energy. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by $\rho_I/\rho_f=(H_I/H_f)^{2} \sim 10^{122}$, a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the $\Lambda$ growth index, $\gamma_{\Lambda} \simeq 6/11$. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a $\chi^{2}$ statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.Comment: 12 pages, 3 figures, accepted for publication by Phys. Rev. D. (final version, some references have corrected). arXiv admin note: substantial text overlap with arXiv:1106.193

The Hamburg/SAO survey for low metallicity blue compact/HII-galaxies (HSS-LM). I. The first list of 46 strong-lined galaxies

We present the description and the first results of a new project devoted to the search for extremely metal-deficient blue compact/HII-galaxies (BCGs) and to the creation of a well selected large BCG sample with strong emission lines. Such galaxies should be suitable for reliable determination of their oxygen abundance through the measurement of the faint [OIII]4363A line. The goals of the project are two-fold: a) to discover a significant number of new extremely metal-poor galaxies (Z <= 1/20 Zo), and b) to study the metallicity distribution of local BCGs. Selection of candidates for follow-up slit spectroscopy is performed on the database of objective prism spectra of the Hamburg Quasar Survey. The sky region is limited by delta >= 0 deg. and b^ii <= -30 deg. In this paper we present the results of the follow-up spectroscopy conducted with the Russian 6m telescope. The list of observed candidates contained 52 objects, of which 46 were confirmed as strong-lined BCGs (EW([OIII]5007) >= 100 A). The remaining five lower excitation ELGs include three BCGs, and two galaxies classified as SBN (Starburst Nucleus) and DANS (Dwarf Amorphous Nucleus Starburst). One object is identified as a quasar with a strong Ly_alpha emission line near 5000 A (z~3). We provide a list with coordinates, measured radial velocities, B-magnitudes, equivalent widths EW([OIII]5007) and EW(H_beta) and for the 46 strong-lined BCGs the derived oxygen abundances 12+log(O/H). The abundances range between 7.42 and 8.4 (corresponding to metallicities between 1/30 and 1/3 Zo). The sample contains four galaxies with Z < 1/20 Zo, of which three are new discoveries.Comment: 19 pages, 13 figures, accepted for publication in A&A, corrected typos, reference

Density of states in the non-hermitian Lloyd model

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-hermitian random ``Hamiltonian''. However, finding the density of states of a non-hermitian random ``Hamiltonian'' remains an open problem, contrary to previous findings in the literature.Comment: 6 pages, RevTex, two-column