Phase separation near half-filling point in superconducting compounds

We present the model of superconducting ceramics using the single band extended Hubbard Hamiltonian. We investigate the simultaneous presence of antiferromagnetism (AF) and d-wave superconductivity (SC) in the coherent potential (CP) approximation applied to the on-site Coulomb repulsion $U$. We consider the hopping interaction, $\Delta t$, the inter-site charge-charge interaction, $V$, (creating SC), and the single site Hund's type exchange interaction, $F_{in}$, (creating AF). The influence of these interactions on the separation of superconducting and antiferromagnetic phases near the half-filling point is investigated. Results are compared with the experimental data for YBaCuO and NdCeCuO compounds.Comment: 4 pages, 4 figure

Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps

We introduce and study the distribution of an estimator for the normalized bispectrum of the Cosmic Microwave Background (CMB) anisotropy. We use it to construct a goodness of fit statistic to test the coadded 53 and 90 GHz COBE-DMR 4 year maps for non-Gaussianity. Our results indicate that Gaussianity is ruled out at the confidence level in excess of 98%. This value is a lower bound, given all the investigated systematics. The dominant non-Gaussian contribution is found near the multipole of order $\ell=16$. Our attempts to explain this effect as caused by the diffuse foreground emission from the Galaxy have failed. We conclude that unless there exists a microwave foreground emission which spatially correlates neither with the DIRBE nor Haslam maps, the cosmological CMB anisotropy is genuinely non-Gaussian.Comment: 16 pages, 3 figs uses aasms4.tex, revised and accepted to Ap. J. Let

Power Spectrum Estimators For Large CMB Datasets

Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very serious challenge to analysing them with existing or anticipated computers. Here we present an investigation of the currently favored algorithm for obtaining the power spectrum from a sky-temperature map --- the quadratic estimator. We show that, whilst improving on direct evaluation of the likelihood function, current implementations still inherently scale as the equivalent of the cube of the number of pixels or worse, and demonstrate the critical importance of choosing the right implementation for a particular dataset.Comment: 8 pages LATEX, no figures, corrected misaligned columns in table

Correlating Fourier phase information with real-space higher order statistics

We establish for the first time heuristic correlations between harmonic space phase information and higher order statistics. Using the spherical full-sky maps of the cosmic microwave background as an example we demonstrate that known phase correlations at large spatial scales can gradually be diminished when subtracting a suitable best-fit (Bianchi-) template map of given strength. The weaker phase correlations lead in turn to a vanishing signature of anisotropy when measuring the Minkowski functionals and scaling indices in real-space and comparing them with surrogate maps being free of phase correlations. Those investigations can open a new road to a better understanding of signatures of non-Gaussianities in complex spatial structures by elucidating the meaning of Fourier phase correlations and their influence on higher order statistics.Comment: 6 pages plus 1 supplemental page, 4 figures, submitte

Band magnetism with inter-site correlations and interactions

We introduce the Hamiltonian to describe narrow band electrons. The physics of driving forces towards ferromagnetism is re-examined. Using different approximations it has been shown that the magnetic moments created by inter-site interaction and inter-site kinetic correlation decrease quickly with temperature. As a result of these interactions and the realistic density of states (DOS) the Curie temperatures calculated after fitting magnetic moments to their low temperature values are realistic. In the past the Curie temperatures calculated using only the on-site interaction were much higher than the experimental temperatures.Comment: 6 pages, 1 figur

Markov Chain Beam Randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation

We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, which we call Markov Chain Beam Randomization, MCBR, randomly samples from a set of templates or functions that describe the beam uncertainties. The method is much faster than direct numerical integration over systematic `nuisance' parameters, and is not restricted to simple, idealized cases as is analytic marginalization. It does not assume the data are normally distributed, and does not require Gaussian priors on the specific systematic uncertainties. We show that MCBR properly accounts for and provides the marginalized errors of the parameters. The method can be generalized and used to propagate any systematic uncertainties for which a set of templates is available. We apply the method to the Planck satellite, and consider future experiments. Beam measurement errors should have a small effect on cosmological parameters as long as the beam fitting is performed after removal of 1/f noise.Comment: 17 pages, 23 figures, revised version with improved explanation of the MCBR and overall wording. Accepted for publication in Astronomy and Astrophysics (to appear in the Planck pre-launch special issue