Elétrons fortemente correlacionados na vizinhança de uma transição de fase quântica

The aim of this work is to derive theWard Identity for the low energy effective theory of a fermionic system in the presence of a hyperbolic Fermi surface coupled with a U(1) gauge field in 2+1 dimensions. These identities are important because they establish requirements for the theory to be gauge invariant. We will see that the identity associated Ward Identity (WI) of the model is not preserved at 1-loop order. This feature signalizes the presence of a quantum anomaly. In other words, a classical symmetry is broken dynamically by quantum fluctuations. Furthermore, we are considering that the system is close to a Quantum Phase Transitions and in vicinity of a Quantum Critical Point the fermionic excitations near the Fermi surface, decay through a Landau damping mechanism. All this ingredients need to be take explicitly to account and this leads us to calculate the vertex corrections as well as self energies effects, which in this way lead to one particle propagators which have a non-trivial frequency dependence

Sistemas Nanoestruturados: Heteroestruturas Quasi-Periódicas de Nitretos e Cálculos Ab initio em Polimorfos CaCO3

The physical properties and the excitations spectrum in oxides and semiconductors materials are presented in this work, whose the first part presents a study on the confinement of optical phonons in artificial systems based on III-V nitrides, grown in periodic and quasiperiodic forms. The second part of this work describes the Ab initio calculations which were carried out to obtain the optoeletronic properties of Calcium Oxide (CaO) and Calcium Carbonate (CaCO3) crystals. For periodic and quasi-periodic superlattices, we present some dynamical properties related to confined optical phonons (bulk and surface), obtained through simple theories, such as the dielectric continuous model, and using techniques such as the transfer-matrix method. The localization character of confined optical phonon modes, the magnitude of the bands in the spectrum and the power laws of these structures are presented as functions of the generation number of sequence. The ab initio calculations have been carried out using the CASTEP software (Cambridge Total Sequential Energy Package), and they were based on ultrasoft-like pseudopotentials and Density Functional Theory (DFT). Two di®erent geometry optimizations have been e®ectuated for CaO crystals and CaCO3 polymorphs, according to LDA (local density approximation) and GGA (generalized gradient approximation) approaches, determining several properties, e. g. lattice parameters, bond length, electrons density, energy band structures, electrons density of states, e®ective masses and optical properties, such as dielectric constant, absorption, re°ectivity, conductivity and refractive index. Those results were employed to investigate the confinement of excitons in spherical Si@CaCO3 and CaCO3@SiO2 quantum dots and in calcium carbonate nanoparticles, and were also employed in investigations of the photoluminescence spectra of CaCO3 crystal

Estudo teórico QTAIM e DFT dos compostos de coordenação: efeito quelato, titanocenos e ligação química

This work is a study of coordination compounds by quantum theory of atoms in molecules (QTAIM), based on the topological analysis of the electron density of molecular systems, both theoretically and experimentally obtained. The coordination chemistry topics which were studied are the chelate effect, bent titanocene and chemical bond in coordination complexes. The chelate effect was investigated according to topological and thermodynamic parameters. The exchange of monodentate ligands on polydentate ligands from same transition metal increases the stability of the complex both from entropy and enthalpy contributions. In some cases, the latter had a higher contribution to the stability of the complex in comparison with entropy. This enthalpic contribution is explained according to topological analysis of the M-ligand bonds where polidentate complex had higher values of electron density of bond critical point, Laplacian of electron density of bond critical point and delocalization index (number of shared electrons between two atoms). In the second chapter, was studied bent titanocenes with bulky cyclopentadienyl derivative π-ligand. The topological study showed the presence of secondary interactions between the atoms of π-ligands or between atoms of π-ligand and -ligand. It was found that, in the case of titanocenes with small difference in point group symmetry and with bulky ligands, there was an nearly linear relationship between stability and delocalization index involving the ring carbon atoms (Cp) and the titanium. However, the titanocene stability is not only related to the interaction between Ti and C atoms of Cp ring, but secondary interactions also play important role on the stability of voluminous titanocenes. The third chapter deals with the chemical bond in coordination compounds by means of QTAIM. The quantum theory of atoms in molecules so far classifies bonds and chemical interactions in two categories: closed shell interaction (ionic bond, hydrogen bond, van der Waals interaction, etc) and shared interaction (covalent bond). Based on topological parameters such as electron density, Laplacian of electron density, delocalization index, among others, was classified the chemical bond in coordination compounds as an intermediate between closed shell and shared interactions

Utilizando mapas de conectividade fuzzy no desenvolvimento de algoritmos reparadores de imagens binárias 3D

A 3D binary image is considered well-composed if, and only if, the union of the faces shared by the foreground and background voxels of the image is a surface in R3. Wellcomposed images have some desirable topological properties, which allow us to simplify and optimize algorithms that are widely used in computer graphics, computer vision and image processing. These advantages have fostered the development of algorithms to repair bi-dimensional (2D) and three-dimensional (3D) images that are not well-composed. These algorithms are known as repairing algorithms. In this dissertation, we propose two repairing algorithms, one randomized and one deterministic. Both algorithms are capable of making topological repairs in 3D binary images, producing well-composed images similar to the original images. The key idea behind both algorithms is to iteratively change the assigned color of some points in the input image from 0 (background)to 1 (foreground) until the image becomes well-composed. The points whose colors are changed by the algorithms are chosen according to their values in the fuzzy connectivity map resulting from the image segmentation process. The use of the fuzzy connectivity map ensures that a subset of points chosen by the algorithm at any given iteration is the one with the least affinity with the background among all possible choices

Espectros fractais em sistemas nanoestruturados e cristais fotônicos

The study of the elementary excitations such as photons, phonons, plasmons, polaritons, polarons, excitons and magnons, in crystalline solids and nanostructures systems are nowdays important active field for research works in solid state physics as well as in statistical physics. With this aim in mind, this work has two distinct parts. In the first one, we investigate the propagation of excitons polaritons in nanostructured periodic and quasiperiodic multilayers, from the description of the behavior for bulk and surface modes in their individual constituents. Through analytical, as well as computational numerical calculation, we obtain the spectra for both surface and bulk exciton-polaritons modes in the superstructures. Besides, we investigate also how the quasiperiodicity modifies the band structure related to the periodic case, stressing their amazing self-similar behavior leaving to their fractal/multifractal aspects. Afterwards, we present our results related to the so-called photonic crystals, the eletromagnetic analogue of the electronic crystalline structure. We consider periodic and quasiperiodic structures, in which one of their component presents a negative refractive index. This unusual optic characteristic is obtained when the electric permissivity and the magnetic permeability µ are both negatives for the same range of angular frequency ω of the incident wave. The given curves show how the transmission of the photon waves is modified, with a striking self-similar profile. Moreover, we analyze the modification of the usual Planck´s thermal spectrum when we use a quasiperiodic fotonic superlattice as a filter.