General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL

We present a detailed implementation of two bispectrum estimation methods which can be applied to general non-separable primordial and CMB bispectra. The method exploits bispectrum mode decompositions on the domain of allowed wavenumber or multipole values. Concrete mode examples constructed from symmetrised tetrahedral polynomials are given, demonstrating rapid convergence for known bispectra. We use these modes to generate simulated CMB maps of high resolution (l > 2000) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient and general f_NL estimator for a given theoretical model. The estimator has two versions comparing theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies, lensing and cosmic strings. We provide examples and validation of both f_NL estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we show how the full bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter F_NL for more consistent comparison between theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model from both our primordial and late-time estimators which are consistent with each other, as well as with results already published in the literature. These general bispectrum estimation methods should prove useful for the analysis of nonGaussianity in the Planck satellite data, as well as in other contexts.Comment: 41 pages, 17 figure

Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the non-analyticity of the fidelity is directly related to the non-analyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually non-commuting Hamiltonians, we analyze the structure of the system's eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically non-trivial Uhlmann mixed state geometric phase.Comment: 18 pages, 8 figures. Version to be publishe

False Vacuum Transitions - Analytical Solutions and Decay Rate Values

In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. Phase transitions are achieved from the associated fluctuation determinant, by the decay rates of the false vacuum.Comment: 6 pages, improved to match the final version to appear in EP

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

A computationally efficient method for calculating the maximum conductance of disordered networks: Application to 1-dimensional conductors

Random networks of carbon nanotubes and metallic nanowires have shown to be very useful in the production of transparent, conducting films. The electronic transport on the film depends considerably on the network properties, and on the inter-wire coupling. Here we present a simple, computationally efficient method for the calculation of conductance on random nanostructured networks. The method is implemented on metallic nanowire networks, which are described within a single-orbital tight binding Hamiltonian, and the conductance is calculated with the Kubo formula. We show how the network conductance depends on the average number of connections per wire, and on the number of wires connected to the electrodes. We also show the effect of the inter-/intra-wire hopping ratio on the conductance through the network. Furthermore, we argue that this type of calculation is easily extendable to account for the upper conductivity of realistic films spanned by tunneling networks. When compared to experimental measurements, this quantity provides a clear indication of how much room is available for improving the film conductivity.Comment: 7 pages, 5 figure

Uso da técnica da solarização como alternativa para o preparo do solo ou substrato para produção de mudas isentas de patógenos de solo.

O preparo de um solo ou substrato para o plantio de mudas sadias é extremamente importante, pois devem estar isentos de fitonematóides, pragas, doenças fúngicas e/ou bacterianas ou de sementes de plantas daninhas. Da mesma forma, o preparo desse substrato deve seguir a correta metodologia, de forma modo a preservar a população de micro-organismos benéficos vivos que garantirão a qualidade dos materiais que devam ser decompostos, fornecendo substâncias as quais que poderão aumentar a resistência das plantas a doenças e pragas, bem como auxiliar no controle biológico dessas pragas. Uso da técnica da solarização como alternativa para o preparo do solo.A esterilização dos solos ou substratos pode ser feita por produtos químicos. Porém, em sua maioria, esses produtos fumigantes têm sido banidos do mercado não somente em conseqüência às restrições ambientais, mas, também, à exigência do consumidor, por produtos de qualidade e sem riscos de contaminação por resíduos químicos. A desinfestação dos solos ou substratos por meio de produtos químicos, principalmente com defensivos de amplo espectro de ação, pode afetar a população de micro-organismos benéficos à cultura, bem como apresentar problemas quanto ao custo, eficiência e trazer contaminações ao ambiente e ao aplicador. Ademais, seu uso pode promover a seleção de patógenos cada vez mais resistentes a esses produtos químicos aplicados, bem como o envelhecimento da terra.bitstream/item/25503/1/cartilharitzinger.pd