In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several techniques from functional analysis and operator algebras have been exploited and specialised to the context of Schrödinger operators and quantum spin systems. Their semi-classical properties including the possible occurrence of SSB have been investigated and illustrated with various physical models. Furthermore, it has been shown that the application of perturbation theory sheds new light on symmetry breaking in Nature, i.e. in real, hence finite materials. A large number of physically relevant results have been obtained and presented by means of diverse research papers.

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In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.

In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho, os efeitos de um campo magnético oblíquo externo no modelo de Gross- Neveu (2+1)-dimensional, que inclui as componentes paralela e perpendicular do campo em relação ao sistema, são estudados no contexto da simetria quiral e discreta do modelo. Nosso principal interesse está nos efeitos deste campo sobre o diagrama de fase do sistema, onde também incluímos os efeitos combinados de temperatura e potencial químico. Os diagramas de fase são obtidos através do potencial efetivo a 1 loop para o modelo, derivado em primeira ordem na expansão 1=N. Transições de fase relevantes que podem ser estudadas através deste modelo são, por exemplo, metal-isolante em matéria condensada e na teoria quântica de campos de férmions planares em geral. A relação entre a transição de fase com quebra da simetria quiral e discreta e o surgimento de um gap (ou a presença de um valor esperado no vácuo do campo escalar diferente de zero), como função do campo magnético oblíquo, é analisada em detalhes. / In this work, the effects of an external oblique magnetic field in the (2+1)-dimensional Gross-Neveu model, and that therefore includes both parallel and perpendicular components of the applied field, are studied in the context of the models discrete chiral symmetry. Our main concern is in the effects of such a field in the systems phase diagram and that also includes the combined effects of temperature and chemical potential. The phase diagrams are obtained through the one-loop effective potential for the model, derived in the leading order in the 1=N expansion Relevant phase transitions that can be studied through this model are, for example, metal-insulator ones in condensed matter and in the quantum field theory of planar fermions in general. The relation between the phase transition with (discrete) chiral symmetry breaking and the emergence of a gap (or the presence of a chiral nonvanishing vacuum expectation value) in the planar fermionic system, as a function of the external oblique magnetic field, is analyzed in details.

La notion de symétrie de jauge est au coeur de notre compréhension de l'interaction électrofaible et permet d'expliquer l'ensemble des observations expérimentales actuelles. Pourtant, l'incompatibilité intrinsèque entre l'invariance de jauge et la masse des particules nécessite d'introduire une nouvelle particule, le boson de Higgs, toujours non observée à ce jour. Cette thèse présente l'analyse de 7.3/fb de collisions protons-antiprotons à sqrt{s} = 1.96 TeV enregistrées par le détecteur D0 au Tevatron en vue de la recherche du boson de Higgs dans l'état final mu+tau. Cette analyse vient compléter les canaux principaux dimuons, électron-muon et diélectrons en exploitant également la désintégration H -> WW -> lvlv, majoritaire dans la fenêtre de masse accessible au Tevatron. L'état final contenant un lepton tau, leur identification parmi les jets a été améliorée d'environ 15% grâce au développement de plusieurs idées : l'ajustement des paramètres du réseau de neurones d'identification, la prise en compte de certaines dépendances cinématiques des performances de l'algorithme, l'exploitation du temps de vie du lepton tau et une étude exhaustive visant à inclure la mesure du détecteur de pieds de gerbe dans le processus d'identification. Dans un second temps, la recherche du boson de Higgs dans l'état final mu+tau étant dominée par le bruit de fond W+jets (où un jet est faussement identifié comme un lepton tau), une méthode a été élaborée pour obtenir une modélisation convenable de ce bruit de fond, non fournie par la simulation par défaut. Cette méthode est basée, entre autres, sur l'étude de la corrélation de charge entre le muon et le candidat tau qui permet de mesurer ce bruit de fond dans les données en excluant la région du signal. Ensuite, l'exploitation des cinématiques et/ou topologies différentes du signal et du bruit de fond a permis d'optimiser cette recherche atteignant alors une sensibilité attendue (observée) de 7.8 (6.6) fois le Modèle Standard pour une masse de 165 GeV/c2. Enfin, l'interprétation de l'analyse dans un scénario à quatre familles de fermions a été effectuée. Pour la première fois, cette analyse est incluse dans les combinaisons D0 et Tevatron présentées à Moriond EW et EPS 2011. / The gauge symmetry is the heart of our understanding of the electroweak interaction and describes all the current experimental results. However, the intrinsic incompatibility between the gauge invariance and the mass of particles leads to the introduction of a new particle, the Higgs boson, for which we have no experimental evidence as of today. This thesis describes the Higgs boson search in the mu+tau final state in 7.3/fb of protons-antiprotons collisions at sqrt{s} = 1.96 TeV collected by the D0 detector at the Tevatron. This analysis completes the golden channels (dimuons, electron-muon, dielectrons) exploiting the decay chain H-> WW ->lvlv, which is the main Higgs boson decay mode in the mass window accessible to the Tevatron. Since the final state includes a tau lepton, work was done to improve their identification among jets. An increase of 15% was achieved thanks to the the following : changing tuning parameters for the tau identification neural network, use of the kinematical dependence of the algorithm performances, incorporation of the tau lepton life time information and full study of the additionnal information coming from the central preshower measurements. Then, since the dominant background of the mu+tau Higgs boson search is W+jets (where one jet fakes a tau), a method was developed to obtain good modeling of this background, not provided by the default simulation. This method is based, among other things, on the charge correlation between the muon and the tau candidate which allows for calibration of this background in the data excluding the signal region. Finally, all the kinematic and/or topological differences between the signal and the background were exploited to optimize this search, reaching an (observed) expected sensitivity of 7.8 (6.6) times the Standard Model for mH = 165 GeV/c2. In addition, this result was also interpreted in a fourth fermion generation scenario. For the first time, this analysis is included in the D0 and Tevatron combinations, both presented at Moriond EW and EPS 2011.

Le comportement thermomécanique des matériaux à mémoire de forme est étudié dans la plage de leur pseudoélasticité. En effet, le modèle Zaki-Moumni initialement validé dans les conditions de chargements quasi statiques, est étendu à l'effet de la vitesse de chargement par la prise en compte du couplage thermomécanique. Les résultats de la simulation de cette extension sont comparés à l'expérience et montre une bonne reproduction qualitative des observations à différentes vitesses de chargements et à température initiale fixée. Le modèle tridimensionnel est ensuite réduit pour analyser les oscillations unidimensionnelles d'un dispositif en matériaux à mémoire de forme. La réponse en fréquences de l'oscillateur forcé est alors investie autour de la résonance. Les oscillations isothermes et non isothermes ainsi que la dissymétrie en traction-compression de la force de rappel, sont prises en compte. Des phénomènes dynamiques tels que le chaos, le doublement de périodes et les sauts autour de bifurcations dans la solution, apparaissent pour des amplitudes de chargement élevées et pour des paramètres matériaux donnés.

No description available.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T13:00:44Z No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) / Made available in DSpace on 2017-09-12T13:00:44Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) Previous issue date: 2016-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this thesis, we study the influence of gravitating non-Abelian cosmic strings on the spacetime geomerty. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically to determine the behaviour for the Higgs, gauge and metric fields. This model under consideration present two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling. So, we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as function of the energy scale where the gauge symmetry is spontaneously broken. We have extented this analysis to de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also for the metric tensor for specific values of the physical parameters of the theory. For de Sitter case, we find the appearance of horizons that although being consequence of the presence of the cosmological constant it strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (tt) and (zz) components of the metric tensor. They present a strongly increasing for large distance from the string. / Nesta tese estudamos a influência das cordas cósmicas não-Abelianas na geometria do espaço-tempo. Para este fim, utilizamos um modelo de Higgs não-Abeliano acoplado com a gravidade e obtemos um sistema de equações diferenciais não-lineares. Como este sistema de equações diferenciais não possui solução analítica, realizamos análise numérica para obter o comportamento dos campos de Higgs, de gauge e métricos em função da distância à corda cósmica. O modelo considerado apresenta dois campos bosônicos e um campo de gauge não-Abeliano. Como os dois setores bosônicos podem apresentar um acoplamento direto, investigamos a relevância deste acoplamento no sistema, especificamente na densidade linear de energia e no déficit de ângulo planar. Também analisamos o comportamento destas quantidades como função da escala de energia onde a simetria de gauge é espontaneamente quebrada. Ampliamos este estudo para as cordas cósmicas não-Abelianas no espaço-tempo de de Sitter e anti-de Sitter. Para isto, construímos um sistema de equações de campo considerando a presença da constante cosmológica. Utilizando a análise numérica, fornecemos o comportamento dos campos de Higgs, de gauge e dos campos métricos para valores específicos dos parâmetros físicos do modelo. Para o caso do espaço-tempo de de Sitter, salientamos o surgimento do horizonte cosmológico que, embora seja consequência da constante cosmológica, está fortemente relacionado ao acoplamento gravitacional. Para o espaço-tempo de anti-de Sitter, encontramos que o sistema não apresenta horizonte. Esta característica do sistema está relacionada às componentes (tt) e (zz) do tensor métrico, que divergem para grandes distâncias da corda cósmica.

Made available in DSpace on 2015-05-14T12:14:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 639748 bytes, checksum: 09ac6e93733c265a01578d25967f780c (MD5) Previous issue date: 2009-10-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we develop some phenomenological aspects of a model based on the gauge symmetry SU(3)CNSU(3)LNU(1)N (311νR), that include righthanded neurinos in its matter content. We establish all the necessary structure for the study of the phenomenological aspects of the model. First, we obtain bounds on the angle that mix the gauge bosons Z and Z′, taking into account a requirement of the model, namely, that the number of fermionic families is exactly three. Also we implement the mass for both species of neutrinos (left-hand and right-handed) via type II seesaw mechanism, obtained adding to the model a sextet of scalars which will be responsible by the violation of the lepton number. The main consequence is the rising of a sterile neutrino with mass in the KeV range, satisfying all the cosmological and astrophysical constraints. This neutrino will a viable candidate for warm dark matter in the universe. / Nesta tese, desenvolvemos alguns aspectos relacionados `a fenomenologia de um modelo com simetria de gauge SU(3)CNSU(3)LNU(1)N (331νR), que possui neutrinos de m ao direita no seu conte´udo de mat´eria. Estabelecemos toda a estrutura necess´aria para o estudo dos aspectos fenomenol´ogicos do modelo. Primeiro, vamos obter v´ınculos no angulo que mistura os b´osons de gauge Z e Z′, levando em conta uma exig encia imposta pelo modelo, ou seja, que o n´umero de fam´ılias fermi onicas ´e exatamente tr es. Tamb´em implementamos termos de massa para ambas as esp´ecies de neutrinos (m ao esquerda e m ao dieita) via mecanismo seesaw tipo II, obtido adicionado ao modelo um sexteto de escalares, que ser´a respons ´avel pela viola¸c ao do n´umero lept onico. A principal consequ encia ´e o surgimento de um neutrino est´eril com massa na escala de KeV , satisfazendo todas as restri¸c oes cosmol´ogicas e astrof´ısicas. Esse neutrino ser´a um vi´avel candidato `a mat´eria escura morna do universo.