[pt] Nesta dissertação utilizamos um modelo baseado na teoria de fenômenos críticos para explicar a formação de preços de ativos financeiros no período précrash. A evolução dos preços é descrita por um crescimento lento em forma de lei de potência, superposto a oscilações periódicas em escala logarítmica, sendo denominado modelo log-periódico. Este crescimento é eventualmente interrompido por um colapso dos preços que ocorre em um curto e crítico intervalo de tempo.O objetivo deste trabalho é o de investigar o modelo logperiódico do ponto de vista econométrico, criticando e propondo melhoramentos na sua especificação de forma que as inferências estatísticas dos seus parâmetros sejam mais confiáveis. Baseado nesta análise é proposta uma extensão do modelo log-periódico, com a incorporação de estrutura auto- regressiva e heterocedástica condicional no termo aleatório do modelo original. O modelo é aplicado a índices de diversos mercados mundiais, a saber: HANG SENG (Hong Kong), NASDAQ (EUA), IBOVESPA (Brasil), MERVAL (Argentina), INDIA BSE NATIONAL (Índia) e FTSE100 (Grã-Bretanha). Os nossos resultados indicam que a utilização destes modelos na prática requer alguma cautela uma vez que a sua base inferencial é frágil. / [en] In this work we employ a model based on the critical phenomena theory to explain the asset price formation associated to the pre- crash period. The evolution of the price is given by an over-all power law acceleration decorated by oscillations called log-periodic model. This growth is likely to be interrupted by a crash of prices that happen in a short and critical time interval. The purpose of this work is to investigate the log-periodic model within the econometric approach by suggesting guidelines to achieve its performance in order to accomplish reliable statistical inferences. Based on this analysis we here propose a stretching of the log-periodic model through the introduction of an autoregressive structure and an autoregressive conditional heteroskedasticity at the residual of the original model. The current model is applied to the study of financial index of the stock markets worldwide as: HANG SENG (Hong Kong), NASDAQ (USA), IBOVESPA (Brazil), MERVAL (Argentina), INDIA BSE NATIONAL (India) and FTSE100 (United Kingdom). The output of such work indicates that the use of the logperiodic model requires some care as far as its inference basis is fragile.

<p>Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting.</p><p>Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality.</p><p>Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.</p>

Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting. Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality. Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.

In this dissertation, I have studied theoretical problems in statistical physics and electrodynamics of Bose particles, namely, mesoscopic effects in statistics of Bose- Einstein condensate (BEC) of atoms and electromagnetic waveguide effects of planar Bragg structures in Free Electron Lasers. A mesoscopic system of a trapped gas of Bose atoms is the most difficult for the theoretical analysis in quantum statistical physics since it cannot be studied by neither a quantum mechanics of the simple microscopic systems of one or very few atoms nor a standard statistical physics of the macroscopic systems that implies a thermodynamic limit. I present analytical formulas and numerical calculations for the moments and cumulants of BEC fluctuations in both ideal and weakly interacting gas. I analyze the universal scaling and structure of the BEC statistics in a mesoscopic ideal gas in the critical region. I present an exactly solvable Gaussian model of BEC in a degenerate interacting gas and its solution that confirms the universality and constraint-cut-off origin of the strongly non-Gaussian BEC statistics. I consider a two-energy-level trap with arbitrary degeneracy of an upper level and find an analytical solution for the condensate statistics in a mesoscopic ideal gas. I show how to model BEC in real traps by BEC in the two-level or three-level traps. I study wave propagation in the open oversized planar Bragg waveguides, in particular, in a planar metal waveguide with corrugation. I show that a step perturbation in a corrugation phase provides a high selectivity over transverse modes. I present a new Free Electron Laser (FEL) amplifier scheme, in which the radiation is guided by the planar Bragg structure with slightly corrugated walls and a sheet electron beam is traveling at a significant angle to the waveguide axis. By means of nonlinear analysis, I demonstrate that the proposed scheme provides an effective mode filtration and control over the structure of the output radiation and allows one to achieve amplification up to 30 dB in the existing FEL machines.

Diese Arbeit befaßt sich mit der Koppelung von Vertex-Modellen an die planaren $\phi^4$-Zufallsgraphen des Zugangs zur Quantengravitation über dynamische Polygonifizierungen. Das betrachtete System hat eine doppelte Bedeutung, einerseits als die Koppelung einer konformen Feldtheorie mit zentraler Ladung $C=1$ an zweidimensionale Euklidische Quantengravitation, andererseits als Anwendung von geometrischer, "annealed" Unordnung auf ein prototypisches Modell der statistischen Mechanik. Da das Modell mit Hilfe einer großangelegten Reihe von Monte Carlo Simulationen untersucht wird, müssen entsprechende Techniken für die Simulation von dynamischen Quadrangulierungen bzw. die dualen $\phi^4$-Graphen entwickelt werden. Hierzu werden verschiedene Algorithmen und die dazugehörigen Züge vorgeschlagen und hinsichtlich ihrer Ergodizität und Effizienz untersucht. Zum Vergleich mit exakten Ergebnissen werden die Verteilung der Koordinationszahlen bzw. bestimmte Analoga davon konstruiert. Für Simulationen des $F$-Modells auf $\phi^4$-Zufallsgraphen wird ein Ordnungsparameter für den antiferroelektrischen Phasenübergang mit Hilfe einer Plakettenspindarstellung formuliert. Ausführliche "finite-size scaling"-Analysen des Kosterlitz-Thouless-Phasenübergangs des $F$-Modells auf dem Quadratgitter und auf Zufallsgraphen werden vorgestellt und die Positionen der jeweiligen kritischen Punkte sowie die dazugehörigen kritischen Exponenten werden bestimmt. Die Rückreaktion des Vertex-Modells auf die Zufallsgraphen wird in Form der Koordinationszahlverteilung, der Verteilung der "Baby-Universen" und dem daraus resultierenden String-Suszeptibilitäts-Exponenten sowie durch die geometrische Zweipunktfunktion analysiert, die eine Schätzung der intrinsischen Hausdorff-Dimension des gekoppelten Systems liefert. / In this thesis, the coupling of ice-type vertex models to the planar $\phi^4$ random graphs of the dynamical polygonifications approach to quantum gravity is considered. The investigated system has a double significance as a conformal field theory with central charge $C=1$ coupled to two-dimensional Euclidean quantum gravity and as the application of a special type of annealed connectivity disorder to a prototypic model of statistical mechanics. Since the model is analyzed by means of large-scale Monte Carlo simulations, suitable simulation techniques for the case of dynamical quadrangulations and the dual $\phi^4$ random graphs have to be developed. Different algorithms and the associated update moves are proposed and investigated with respect to their ergodicity and performance. For comparison to exact results, the co-ordination number distribution of the dynamical polygonifications model, or certain analogues of it, are constructed. For simulations of the 6-vertex $F$ model on $\phi^4$ random graphs, an order parameter for its anti-ferroelectric phase transitions is constructed in terms of a "plaquette spin" representation. Extensive finite-size scaling analyses of the Kosterlitz-Thouless point of the square-lattice and random graph $F$ models are presented and the locations of the critical points as well as the corresponding critical exponents are determined. The back-reaction of the coupled vertex model on the random graphs is investigated by an analysis of the co-ordination number distribution, the distribution of "baby universes" and the string susceptibility exponent as well as the geometric two-point function, yielding an estimate for the internal Hausdorff dimension of the coupled system.

Thesis (Ph. D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 52-10, Section: B, page: 5290. Supervisor: M.F. Collins.

Thesis (Ph.D.)--McMaster University, 2004. / Advisor: David Venus. Includes bibliographical references (leaves 138-144). Also available via World Wide Web.

Foi desenvolvido o aparato experimental necessário à realização de experimentos de RMN em baixas temperaturas, com o objetivo de investigar fenômenos críticos nos sistemas antiferromagnéticos diluídos FexZn1-xF2. Estudou-se a dependência do segundo momento da linha de ressonância do F0 com a temperatura, desde T &#8776 TN até T &#8776 250K, através de medidas experimentais e simulações numéricas baseadas num modelo de campo médio. Também foi estudada a dependência angular da meia largura e da forma da linha. Os resultados das simulações numéricas concordam qualitativamente, mas não quantitativamente, com os resultados experimentais. Encontramos também a indicação de uma distribuição em T2 ao longo da linha de ressonância do F0, quando H0 é orientado perpendicularmente ao eixo C. O expoente crítico da magnetização do REIM foi medido diretamente a partir do segundo momento da linha do F0, após um esfriamento da amostra sem campo aplicado (Zero Field Cooling). O resultado obtido &#946=0.36 &#177 0.01 concorda com o valor esperado &#946= 0.35 / The experimental apparatus required for Nuclear Magnetic Resonance low temperatures experiments was developed for the investigation of critical phenomena in the diluted antiferromagnetic FexZn1-xF2. The dependence of the second moment of the F0 resonance line with the temperature was studied from T &#8776 TN to T &#8776 250K, both by experimental measurements and numerical mean field simulations. Angular dependence of the line width and line shape were also investigated. The numerically simulated results qualitatively agreed, but quantitatively didn´t agree with the experimental results. We found an indication of a distribution in T2 through the F0 resonance line, when H0 is oriented perpendicularly to the C axis. The magnetization critical exponent &#946 of the REIM was measured directly from the second moment of the F0 resonance line, after a zero field cooling procedure. We obtained &#946= 0.36 &#177 0.01 which is to be compared with the theoretical value &#946= 0.35

Em decorrência do grande avanço alcançado pela mecânica estatística devido a introdução das idéias de invariância conforme às teorias de escala para sistemas finitos, retomamos, neste trabalho, o estudo do modelo XY em campo transverso. A princípio, apresentamos uma análise detalhada do comportamento \"crossover\" característico do modelo, onde incluímos cálculos melhorados dos expoentes da susceptibilidade e do gap de energia anteriormente apresentados por dos Santos e Stinch-combe. Em seguida, uma análise numérica do espectro foi desenvolvida, considerando-se condições livres de contorno, e comparada com as previsões da invariância conforme. Finalmente, as correções à energia do estado fundamental de cadeias finitas foram utilizadas para obter o parâmetro que caracteriza as classes de universalidade (a carga central c). / In view of the great advance attached from statistical mechanics due to the conformal invariance ideas introduced to the scale theories, we take over at this work, the study of the XY model in a transverse field. At first, we present a detailed analysis on the sample\'s typical crossover behavior. An improved calculation of the susceptibility and gap exponents early presented by dos Santos and Stinchcombe is included. Nest, a numerical analysis of the spectrum, regarding free boundary condi¬tions was developed and compared with conformal invariance predictions. Finally, the fundamental state energy corrections of finite chains were used to obtain the parameter which ,distingoishes the universality classes (the central charge c).

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21551号 / 理博第4458号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 准教授 藤 定義, 准教授 荒木 武昭 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM