In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

Techn. Universiẗat, Diss., 2005--Berlin.

Dans cette thèse nous nous intéressons aux propriétés qualitatives des solutions de quelques équations d’ondes en milieux dispersifs ou dispersifs-dissipatifs. Dans le premier chapitre, nous étudions l’explosion de solutions dans le régime log-log et l’existence globale pour le problème de Cauchy de l’équation de Schrödinger L2-critique amortie. Dans un second chapitre, nous considérons l’équation de Schrödinger L2-critique avec un amortissement non linéaire. Selon la puissance du terme d’amortissement, nous montrons l’existence globale ou l’explosion en régime log-log. Dans le troisième chapitre, nous étudions le problème de Cauchy pour l’équation de Kadomtsev-Petviashvili-Burgers-I (KPBI) en deux dimensions,nous montrons que le problème est localement bien posé dans Hs(R2) pour tout s > -½, et que l’existence est globale dans L2(R2) sans aucune condition sur la donnée initiale. Dans le dernier chapitre, nous considèrons l’équation d’Ostrovsky sur le cercle, et nous construisons des mesures invariantes par le flot selon les quantitées conservées par cette équation. / This thesis deals with the qualitative properties of solutions to some wave equations in dispersive or dispersive-dissipative media. In the first chapter, we study the blowup in the log-log regime and global existence of solutions to the Cauchy problem for the L2-critical damped nonlinear Schrödinger equation. In the second chapter, we consider the Cauchy problem for the L2-critical nonlinear Schrödinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with a log-log blow-up law. In the third chapter, we study the Cauchy problem for the Kadomtsev-Petviashvili-Burgers-I (KPBI) equations in two dimensions. We show that the problem is locally and globally well posed in Hs(R2) for any s > -½ , and that the existence is global in L2(R2) without any condition on the initial data. In the last chapter, we consider the Ostrovsky equation on the circle. We construct invariant measures under the flow for the conserved quantities of the equation.

Downsizing in cars lead to higher noise emissions through the addition of turbo-/superchargers. These noise emissions must be counteracted and cancelled in order to contribute to the overall quality feel of a car. This project follows a product development method in order to research if a new type of silencers are applicable in air induction systems in order to dampen noise emissions. The project also cover how to manufacture the new type of silencers, traditionally used as acoustic insulation in offices. The project covered everything from literature review on silencers, noise regulations, downsizing and traditional plastic manufacturing methods. After the analysis of the results, it stood clear that the new silencers are more effective than conventional solutions. A manufacturing process was also determined, which needs further research in order to derive what the manufacturing cost would be. The project resulted in strong indicators that the new silencers are promising but also opened up to new research questions.

Realizamos nesse trabalho um tratamento abrangente da interação entre um sistema quântico e o meio ambiente modelado como um conjunto de osciladores harmônicos. Partimos para isso de um tratamento prévio de redes de osciladores harmônicos quânticos dissipativos. Utilizando a função característica, transformamos a equação de von Neumann em uma equação diferencial, e explorando a sua linearidade, essa é transformada em uma equação vetorial, cuja resolução é computacionalmente eficiente. Nosso formalismo, que parte de uma rede de osciladores harmônicos, não necessariamente dividida entre sistema e meio ambiente, permite que se contorne a necessidade da hipótese de acoplamento súbito sistema-reservatório para o tratamento exato da evolução do sistema. Em seguida, mostramos que essa evolução pode ser sempre descrita por uma equação mestra na forma usual de Lindblad, embora os coeficientes que a definem possam ser dependentes do tempo. Isso abre novas possibilidades para a dinâmica do sistema, e leva a efeitos que podem ser classificados de não-Markovianos, embora sejam descritos por uma equação mestra completamente local no tempo. Ressaltamos que, por ser baseado em uma solução exata, o método pode ser aplicado para qualquer intensidade de acoplamento, e é consideravelmente mais simples do que outros métodos disponíveis para esse fim, como os baseados em integrais de trajetória. Por fim, utilizamos simulações computacionais para explorar a validade das aproximações de ondas girantes e de Born-Markov, e os fenômenos que podem ser observados nos regimes em que elas deixam de ser válidas. / We present a comprehensive treatment of the interaction of a quantum system with an environment modeled as a set of harmonic oscillators. We start from a previous treatment of a network of quantum dissipative harmonic oscillators. Using the characteristic function, we transform the von Neumann equation in a differential equation, and exploring its linearity, this is transformed in a vector equation, whose solution is computationally efficient. Our method, whose origin lies on a network not necessarily divided into system and reservoir, allows us to circumvent the necessity of the sudden-coupling approximation for the exact treatment of the system evolution. After this, we show that this dynamics can always be described by a master equation in standard Lindblad form, although its coefficients may be functions of time. This opens new possibilities for the system dynamics, and lead to effects that may be called non-Markovian, even if they are described by a completely local-in-time master equation. It should be emphasized that, as it is based on an exact solution, the method may be applied for any strength of the system-reservoir interaction, and it is considerably simpler than other available methods, such as those based on path integrals. Finally, we employ computer simulations to investigate the validity of the rotating-wave and Born-Markov approximations, and the phenomena that migth be observed in regimes in which they fail to be valid.

Este trabalho tem por objetivo avaliar a emissão de metano em dois reservatórios amazônicos, Tucuruí e Samuel. A análise leva em consideração flutuações da área/cota e medidas isotópicas e de fluxos de d13CH4 obtidas em campo, as quais são influenciadas por diversos fatores simultaneamente, como ventos, pressão atmosférica, oxidação na coluna d´água e outros. A composição isotópica do metano em bolhas do sedimento indica que a principal via metanogênica é a redução de CO2. Os resultados também mostram que as emissões em reservatórios rasos são bem mais elevadas que nos mais profundos. Usando conceitos e técnicas da teoria fractal, baseada fundamentalmente em leis de potência, um modelo entre nível de água, área do reservatório e fluxo de metano permitiu estimar a emissão do reservatório de Tucuruí, num horizonte de 100 anos de vida útil, em 2,5 ± 2,7 x 10^6 toneladas de CH4. As emissões locais são amplificadas com a diminuição da cota, porém a emissão total do reservatório diminui, em função da contração da área do reservatório. Num cenário mais otimista, as emissões de Tucuruí em CO2 equivalentes devem ser 0,13 ± 0,14 x 10^6 toneladas de C/ano. / The purpose of this work is evaluating methane emissions from two Amazonian reservoirs, Tucuruí and Samuel. The analysis considers fluctuations of the reservoir area-height and isotopic measurements and fluxes of d13CH4 acquired in the field, which are influenced by many factors simultaneously, such as winds, atmospheric pressure, oxidation in the water column, and others. Isotopic composition of methane in bubbles indicates that CO2 reduction is a major pathway for methane production in the sediments. The results also show that fluxes are higher in shallow reservoirs than in deeper ones. Using concepts and techniques of fractal theory, fundamentally based on power law functions, and considering a time horizon of 100 years, a model between water level, flux and reservoir area of Tucuruí allowed to estimate methane emission from Tucuruí at about 2,5 ± 2,7 x 10^6 tons of CH4. When water levels drop local methane emissions are enhanced, although, total reservoir emission decreases, due to the shrinking of the reservoir area. Over an optimistic scenario, the emissions of Tucuruí reservoir in CO2 equivalents would be around 0,13 ± 0,14 x 10^6 tons C/year.

O presente trabalho apresenta a teoria de sistemas dinâmicos dissipativos impulsivos. Apresentamos resultados suficientes e necessários para obtermos dissipatividade para sistemas impulsivos autônomos e não autônomos utilizando funções de Lyapunov. No que segue, desenvolvemos a teoria de estabilidade para a seção nula de um sistema dinâmico não autônomo com impulsos. Utilizando os resultados da teoria abstrata para sistemas não autônomos com impulsos, apresentamos o estudo da estabilidade de um modelo presa-predador com controle e impulsos. / The present work presents the theory of impulsive dissipative dynamical systems. We present necessary and sufficient conditions to obtain dissipativity for autonomous and non-autonomous impulsive dynamical systems via Lyapunov functions. In the sequel, we develop the theory of stability for the null section of non-autonomous dynamical systems with impulses. Using the results from the abstract theory we present the study of stability for a controlled prey-predator model under impulse conditions.

Made available in DSpace on 2016-08-29T11:13:02Z (GMT). No. of bitstreams: 1 tese_7470_Dissertação - Tales 2015.pdf: 529308 bytes, checksum: 26d5b6dd98391005143ca45f4b5033dd (MD5) Previous issue date: 2015-03-02 / O debate entre os paradigmas da mecânica e o sistêmico tem causado importantes revoluções nos mais diversos campos de conhecimento, principalmente na física, química e biologia. Sendo assim, esta dissertação tem o objetivo de analisar como as teorias sistêmicas mais recentes desenvolvidas na química, a partir de Prigogine, e na biologia, conforme Maturana e Varela, podem contribuir para a abordagem institucionalista de Veblen. Para isso, apoiar-se-á na hipótese fornecida pela Teoria Geral dos Sistemas, de Bertalanffy (2006), no qual se refere que os princípios que regem um determinado sistema independem das particularidades de seus componentes mas do modo como estes se inter-relacionam. Assim, a convergência entre estas três teorias passa a ser válida uma vez que o tipo de sistema tratado em todas seja caracterizado por: 1) irreversibilidade da trajetória de suas mudanças, 2) com oposição à ideia de equilíbrio e 3) a introdução de uma abordagem evolucionária e com tempo histórico. Este trabalho se inicia a partir da introdução ao debate entre os paradigmas da mecânica e sistêmico surgido no ramo da física. Na sequência apresenta os referenciais teóricos do institucionalismo de Veblen e da teoria das estruturas dissipativas e autopoiese. Em seguida é feito a análise de convergência entre os arcabouços teóricos vistos, e verificado como as abordagens de Prigogine juntamente com a de Maturana e Varela podem contribuir para o estudo das instituições. Por fim é mostrado como a abordagem desenvolvida neste trabalho pode auxiliar no tratamento de questões relacionadas à economia, com ênfase dada especificamente no que tange a economia monetária. / The debate between the paradigms of mechanical and systemic has caused important revolutions in various fields of knowledge, especially in physics, chemistry and biology. Thus, this work aims to analyze how the most recent systemic theories developed in chemistry, from Prigogine, and biology, as Maturana and Varela, can contribute to the institutional approach of Veblen. For this, will be supporting the hypothesis provided by General Systems Theory of Bertalanffy (2006), which mentions that the principles governing a given system independent of the peculiarities of its components but how these interrelate . The convergence between these three theories becomes valid once the treaty system in all type is characterized by: 1) irreversibility of the trajectory of your changes, 2) with opposition to the idea of equilibrium and 3) the introduction of a evolutionary and historical time approach. This study starts from the introduction to the debate between the paradigms of mechanical and systemic emerged in the physics branch. Following presents the theoretical frameworks of institutionalism of Veblen and the theory of dissipative structures and autopoiesis. Next up is done the analysis of convergence between visas theoretical frameworks, and verified as the approaches of Prigogine along with Maturana and Varela can contribute to the study of institutions. Finally it is shown how the approach developed in this work can assist in addressing issues related to the economy, with emphasis specifically with respect to monetary economics.

Cette thèse s’articule autour de trois projets principaux indépendants les uns des autres. En premier lieu, nous avons développé une méthode de résolution chirale innovante reposant sur l’écoulement de Taylor-Couette et ne nécessitant donc pas l’utilisation d’une phase stationnaire. Les résultats de cette étude sont présentés dans le chapitre 2. En parallèle, nous nous sommes également investis en chimie supramoléculaire et avons notamment commencé à explorer l’effet d’un faible champ magnétique (< 2 T) sur le processus d’auto-assemblage de motifs moléculaires paramagnétiques. Nos efforts expérimentaux sont consignés dans le chapitre 3, chapitre à la fin duquel nous discutons de l’intérêt des états hors-équilibre dissipatifs, en particulier en chimie supramoléculaire. Ces derniers sont d’ailleurs (encore aujourd’hui) une branche énigmatique de la thermodynamique dans la mesure où de tels systèmes ne sont encore décrits par aucun principe thermodynamique (à l’inverse des systèmes à l’équilibre, parfaitement décrits par la thermodynamique classique) rendant leur prédiction compliquée. Dans le chapitre 4, nous exposons notre tentative de description d’un système dissipatif (un oscillateur de pH tout organique) au moyen de mesures calorimétriques à flux continu. Ces trois projets, bien que très différents, s’articulent néanmoins tous autour d’une philosophie commune : l’auto-assemblage loin de l’équilibre. / This thesis deals with three main projects, which are loosely related to one another. Chapter one introduces the progress made in the field of mechanical chiral resolution. The second chapter of this thesis shows the development of a resolution method based on Taylor-Couette flow, and how nonequilibrium self-assembly amplifies the resolution process. The third chapter describes our efforts to control non-equilibrium self-assembly by using weak magnetic fields (<2T). Finally, in chapter four, we show our attempts to describe non-equilibrium dissipative states using continuous-flow calorimetry. All chapters contain elements of non-equilibrium self-assembly or non-equilibrium systems, hence the title: “Non-equilibrium self-assembly: from shear flows to magnetic fields”

Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.