Contributions of point extragalactic sources to the Cosmic Microwave Background bispectrum

All the analyses of Cosmic Microwave Background (CMB) temperature maps up--to--date show that CMB anisotropies follow a Gaussian distribution. On the other hand, astrophysical foregrounds which hamper the detection of the CMB angular power spectrum, are not Gaussian distributed on the sky. Therefore, they should give a sizeable contribution to the CMB bispectrum. In fact, the first year data of the Wilkinson Microwave Anisotropy Probe (WMAP) mission have allowed the {\it first} detection of the extragalactic source contribution to the CMB bispectrum at 41 GHz and, at the same time, much tighter limits than before to non--Gaussian primordial fluctuations. In view of the above and for achieving higher precision in current and future CMB measurements of non--Gaussianity, in this paper we discuss a comprehensive assessment of the bispectrum due to either uncorrelated and clustered extragalactic point sources in the whole frequency interval around the CMB intensity peak. Our calculations, based on current cosmological evolution models for sources, show that the reduced angular bispectrum due to point sources, $b_{ps}$, should be detectable in all WMAP and Planck frequency channels. We also find agreement with the results on $b_{ps}$ at 41 GHz coming from the analysis of the first year WMAP data. Moreover, by comparing $b_{ps}$ with the primordial reduced CMB bispectrum, we find that only the peak value of the primordial bispectrum (which appears at $l\simeq 200$) results greater than $b_{ps}$ in a frequency window around the intensity peak of the CMB. The amplitude of this window basically depends on the capability of the source detection algorithms (i.e., on the achievable flux detection limit, $S_{lim}$, for sources).Comment: 26 pages, 6 Figures, use AasTex5.0, ApJ, in press, Oct. 10, 2003 Issu

Existence Criterion of Genuine Tripartite Entanglement

In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.Comment: 6 pages, 2 figure

Generalized Wick's theorem for multiquasiparticle overlaps as a limit of Gaudin's theorem

We are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean field wave functions by using the extension of the statistical Wick's theorem (Gaudin's theorem) in the appropriate limits.Comment: 28 page

Separable approximation to two-body matrix elements

Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the transformation to center of mass and relative coordinate (in the spirit of Talmi's method) and therefore it is only useful (finite number of expansion terms) for harmonic oscillator single particle states. The converge of the expansion with the number of terms retained is studied for a Gaussian two body interaction. The limit of a contact (delta) force is also considered. Ways to handle the general case are also discussed.Comment: 10 pages, 5 figures (for high resolution versions of some of the figures contact the author

Those wonderful elastic waves

We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.Comment: 11 Figures 26 page

A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices , each with full column rank. Each matrix is exactly factored as Di = UiΣiVT, where V, identical in all factorizations, is obtained from the eigensystem SV = VΛ of the arithmetic mean S of all pairwise quotients of the matrices , i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λk≥1. Equality holds if and only if the corresponding eigenvector vk is a right basis vector of equal significance in all matrices Di and Dj, that is σi,k/σj,k = 1 for all i and j, and the corresponding left basis vector ui,k is orthogonal to all other vectors in Ui for all i. The eigenvalues λk = 1, therefore, define the “common HO GSVD subspace.” We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified

Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site

Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' particle current versus particle density diagrams are investigated and an explanation for how the finite current goes above a maximum value predicted for infinite systems is found in the canonical ensemble.Comment: 18 pages, 4 figures, revtex