This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. For the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and uncertainties of circuit observables. Macroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits.

This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. For the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and uncertainties of circuit observables. Macroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis addresses the problem of robustness in model predictive control (MPC) of discrete-time systems. In contrast with most previous work on robust MPC, our main focus is on robustness in the face of both imperfect state information and dynamic model uncertainty. For linear discrete-time systems with model uncertainty described by sum quadratic constraints, we propose output-feedback MPC policies that: (i) treat soft constraints using quadratic penalty functions; (ii) respect hard constraints using 'tighter' constraints; and (iii) achieve robust closed-loop stability and non-zero setpoint tracking. Our two main tools are: (1) a new linear matrix inequality condition which parameterizes a class of quadratic MPC cost functions that all lead to robust closed-loop stability; and (2) a new parameterization of soft constraints which has the advantage of leading to optimization problems of prescribable size. The stability test we use for MPC design builds on well-known results from dissipativity theory which we tailor to the case of constrained discrete-time systems. The proposed robust MPC designs are shown to converge to well-known nominal MPC designs as the model uncertainty (description) goes to zero. Furthermore, the present approach to cost function selection is independently motivated by a novel result linking MPC and minimax optimal control theory. Specifically, we show that the considered class of MPC policies are the closed-loop optimal solutions of a particular class of minimax optimal control problems. In addition, for a class of nonlinear discrete-time systems with constraints and bounded disturbance inputs, we propose state-feedback MPC policies that input-to-state stabilize the system. Our two main tools in this last part of the thesis are: (1) a class of N-step affine state-feedback policies; and (2) a result that establishes equivalence between the latter class and an associated class of N-step affine disturbance-feedback policies. Our equivalence result generalizes a recent result in the literature for linear systems to the case when N is chosen to be less than the nonlinear system's 'input-state linear horizon'.

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.

Apresentamos um estudo sobre o fenômeno da decoerência durante a evolução temporal de um estado atômico ao interagir com o campo eletromagnético de uma cavidade não ideal. Apresentamos um modelo em que o campo da cavidade esta acoplado a um banho externo e mostramos os efeitos dissipativos que este acoplamento pode gerar na decoerência para um sistema átomo campo. Discutimos as grandezas relevantes para analise da decoerência através de modelos analíticos e numéricos, principalmente entre os acoplamentos átomo campo e campo banho. Sugerimos que o retardamento observado no processo de decoerência seja uma característica geral em sistemas analisáveis como constituídos de três subsistemas acoplados sequencialmente, com propriedades espectrais e acoplamentos suficientemente assimétricos. / We present a study of the phenomenon of decoherence in the time evolution of an atomic state with the electromagnetic field of a non-ideal cavity. We present a model where the cavity field is coupled to an external bath and show the dissipative effects this coupling can generate in the decoherence of the atom field system. We discuss the relevant variables for the analysis of decoherence in terms of analytic and numerical models, especially the atom-field and field-bath couplings. We suggest that the observed hindrance of the decoherence process may be a general property in systems which can be considered as formed by three subsystems coupled sequentially, with spectral properties and sufficiently asymmetric coupling.

Exciton-polaritons are the fundamental excitations arising from the strong coupling of quantum well excitons and cavity photons in semiconductor microcavities. They are compound bosons for which stimulated scattering and macroscopic occupation of single quantum states can occur at sufficiently high densities. One way of creating such polariton condensates is with nonresonant optical pumping. Doing so creates a large density of free- carriers and excitons that strongly interact and blueshift the polariton energy levels. Using spatially patterned nonresonant fields, the polariton potential landscape can be tailored and optically trapped condensates can be created. This thesis shows that the spin properties of polariton condensates are strongly modified by such trapping. Under linearly polarised pumping, helicity can spontaneously develop at a critical occupation, breaking the parity symmetry. This formation of spin-up/spin-down condensates is explained within a Gross-Pitaevskii model which accurately reproduces the influence of electric fields and condensate density. Under elliptically polarised pumping, two phenomena are observed: the formation of condensates with the opposite handedness to the pump and hysteresis of both occupation and spin with respect to pump power. The spatial dependence of these effects highlights the limitations of commonly used models of polariton condensation. Finally, the suitability of patterned optical fields for the creation of polariton lattices is explored. For small chains of condensates, controllable coupling between adjacent spins is demonstrated, with the formation of antiferromagnetic and ferromagnetic domains. The extent of these domains is strongly affected by sample nonuniformity, fundamentally limiting the scalability of these lattices.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-10T17:19:34Z No. of bitstreams: 1 MISAELLE DO NASCIMENTO OLIVEIRA - DISSERTAÇÃO PPGMAT 2015..pdf: 1209511 bytes, checksum: 5d4b2e49f1d20c974e738f463c1e1165 (MD5) / Made available in DSpace on 2018-08-10T17:19:34Z (GMT). No. of bitstreams: 1 MISAELLE DO NASCIMENTO OLIVEIRA - DISSERTAÇÃO PPGMAT 2015..pdf: 1209511 bytes, checksum: 5d4b2e49f1d20c974e738f463c1e1165 (MD5) Previous issue date: 2015-08 / Capes / O estudo do comportamento assintótico de sistemas dissipativos é um campo de pesquisa em Equações Diferenciais Parciais-EDP. Existem na literatura várias técnicas para abordar o comportamento assintótico. Contudo, o objetivo deste trabalho é aplicar a técnica devido ao resultado obtido por Gearhart (ver Z. Liu e S. Zheng [21]) que consiste em explorar as propriedades dissipativas do semigrupo associado ao sistema. / The study of the asymptotic behavior of dissipative systems is an important part of the research of Partial Di erential Equations-PDE. Consequently, there are various methods to analize this one. The objective of this work is to apply the a result due to Gearhart (see Z. and S. Liu Zheng [21]) which consits in to explore the dissipation properties of the semigroups associated to dissipative systems.

Apresentamos um estudo sobre o fenômeno da decoerência durante a evolução temporal de um estado atômico ao interagir com o campo eletromagnético de uma cavidade não ideal. Apresentamos um modelo em que o campo da cavidade esta acoplado a um banho externo e mostramos os efeitos dissipativos que este acoplamento pode gerar na decoerência para um sistema átomo campo. Discutimos as grandezas relevantes para analise da decoerência através de modelos analíticos e numéricos, principalmente entre os acoplamentos átomo campo e campo banho. Sugerimos que o retardamento observado no processo de decoerência seja uma característica geral em sistemas analisáveis como constituídos de três subsistemas acoplados sequencialmente, com propriedades espectrais e acoplamentos suficientemente assimétricos. / We present a study of the phenomenon of decoherence in the time evolution of an atomic state with the electromagnetic field of a non-ideal cavity. We present a model where the cavity field is coupled to an external bath and show the dissipative effects this coupling can generate in the decoherence of the atom field system. We discuss the relevant variables for the analysis of decoherence in terms of analytic and numerical models, especially the atom-field and field-bath couplings. We suggest that the observed hindrance of the decoherence process may be a general property in systems which can be considered as formed by three subsystems coupled sequentially, with spectral properties and sufficiently asymmetric coupling.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23694号 / 理博第4784号 / 新制||理||1685(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 川上 則雄, 教授 柳瀬 陽一, 教授 高橋 義朗 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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.