This thesis presents two dimensional discrete dynamical system, the extended standard family of maps, which approximates homoclinic bifurcations of continuous dissipative systems. The main subject of study is the problem of separatrix splitting which was first discovered by Poincaré in the context of the n-body problem. Separatrix splitting leads to chaotic behaviour of the system on exponentially small region in parameter space. To estimate the size of the region the dissipative map is extended to complex variables and approximated by differential equation on a specific domain. This approach was proposed by Lazutkin to study separatrix splitting for Chirikov’s standard map. Furthermore the complex nearly periodic function is used to estimate the width of the exponentially small region where chaos prevails and the map is related to the semistandard map. Numerical computations require solving complex differential equation and provide the constants involved in the asymptotic formula for the size of the region. Another problem studied in this thesis is the prevalence of resonance for the dissipative standard map on a specific invariant set, which for one dimensional map corresponds to a circle. The regions in parameter space where periodic behaviour occurs on the invariant set is known as Arnold tongues. The width of Arnold tongue is studied and numerical results obtained by iterating the map and solving differential equation are related to the semistandard map.

A geração e proteção de estados quânticos é fundamental para a mecânica quântica. Usualmente, utilizam-se protocolos de engenharia de estados baseados na aplicação sucessiva de transformações unitárias, cuja performance se torna menos efetiva conforme aumenta-se o número de componentes envolvidos nas transformações (já que transformações unitárias dependem de um elevado número de operações ou transformações com alto grau de fidelidade), além de tornarem-se mais vulneráveis a efeitos de flutuações de parâmetros experimentais, efeitos de desordem, decoerência e ruído. Dentre as possíveis estratégias para gerar estados quânticos, existe a chamada engenharia de interações quânticas, na qual pode-se tanto estudar como alterar a maneira a partir da qual sistemas interagem entre si para produzir um determinado estado estacionário desejado, quanto para investigar propriedades dos estados gerados ao se alterar alguma característica de tal interação. Neste trabalho apresentaremos duas propostas para gerar estados não-clássicos via engenharia de reservatórios (engenharia dissipativa) em dois tipos de sistemas distintos. No primeiro, utilizaremos um sistema optomecânico no qual efetua-se engenharia de dissipação a fim de obter hamiltonianos seletivos com os quais é possível preparar-se estados de Fock sob efeitos dissipativos, no qual mostramos o caráter não clássico dos estados obtidos nos regimes de cavidade altos e baixos fatores de qualidade. No segundo, utilizaremos um sistema de spins na qual podemos obter estados não-clássicos (emaranhados) para um sistema com o número de partículas (N) entre 2 e 12 via engenharia de interações quânticas com caráter coletivo, para obter diversos estados, considerando efeitos dissipativos como dissipações térmicas e defasagem, além de considerar a robustez com relação a flutuações em alguns parâmetros experimentais do modelo. / The generation and protection of quantum states is fundamental to quantum mechanics. Usually, state engineering protocols are used based on the successive application of unitary transformations, whose performance becomes less effective as the number of components involved in the transformations increases (as that depends on a large number of high-fidelity operations), in addition to becoming more vulnerable to the effects of fluctuations of experimental parameters , effects of disorder, decoherence and noise. Among the possible strategies to yield quantum states, there is the so-called quantum interaction engineering, in which one can either study how to change the way in which systems interact with each other to produce a desired steady state, or to investigate properties of the engineered states by changing some characteristic of such interaction. In this work we present a proposal to engineer non-classical states through reservoir engineering (dissipative engineering) in two types of systems. In the first one, we will use an optomechanical system in which dissipative engineering is carried out in order to obtain selective Hamiltonians with whom it is possible to prepare Fock states under dissipative effects, in which we show the non-classical character of the states obtained in the good and bad cavity regimes.. In the second, we will use a spin chain system in which we can obtain non-classical (entangled) states for a system with the number of particles (N) between 2 and 12 via quantum interaction engineering with collective character, to obtain several states, taking into account dissipative effects such as thermal dissipation and dephasing, and showing the robustness in relation to fluctuations in some experimental parameters of the model.

O presente trabalho dedica-se a uma modelagem da interação entre corpos celestes, em regime Newtoniano, levando-se em consideração as influências que suas deformações e viscosidades internas exercem sobre seus movimentos orbitais e suas velocidades angulares. A abordagem adotada é uma variação do conhecido problema do corpo pseudo-rígido, a qual simplifica drasticamente a determinação dos equilíbrios relativos e torna a questão da dinâmica matematicamente acessível. Com este tratamento, podemos relacionar ou comparar os resultados com aqueles estabelecidos na literatura, dentre eles: formato de equilíbrio de um fluido isolado em rotação, deformação de maré causada pela interação gravitacional e o torque de maré induzido no mesmo. Pela simplicidade do modelo pode-se ainda fazer uma análise qualitativa da dinâmica do sistema e obter estimativas sobre a velocidade com que se aproxima dos equilíbrios. / The present work is devoted to model the interaction among celestial bodies, in a Newtonian regime, but considering the role played by the internal deformation and viscosity on the orbital motion and angular velocities of the components of the system. The work is mainly developed with an alternative approach to the pseudo-rigid body model, which simplifies the determination of the relative equilibria and allows precise conclusions about the dynamics. So, we are able to compare the results of this theory with those established in the literature, namely: the equilibrium shape of an isolated fluid in rotation, the tidal elongation induced by gravitational interaction and the tidal torque. Due to its simplicity, we can further perform a qualitative analysis of the dynamics of the system and estimate the velocity of attraction of the equilibrium states.

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.

Made available in DSpace on 2016-12-23T14:08:16Z (GMT). No. of bitstreams: 1 Atilio Barbosa Lourenco.pdf: 1281099 bytes, checksum: 30b11e22aaae3c126ccd46522b08d45e (MD5) Previous issue date: 2012-12-13 / Este trabalho tem como objetivo apresentar uma abordagem termoeconômica alternativa cuja aplicação em ciclos de refrigeração deve isolar equipamentos dissipativos, como condensadores e válvulas, na estrutura produtiva de modo que os resultados gerados sejam coerentes. A abordagem, chamada de Modelo UFS, é baseada no conceito de desagregação da exergia física, no caso, em três componentes, a saber, termo de energia interna, termo de trabalho de fluxo e termo entrópico e é aplicada a cinco ciclos de refrigeração, a saber, ciclo reverso de Carnot, ciclo simples por compressão de vapor, ciclo multipressão por compressão de vapor em cascata, ciclo multipressão por compressão de vapor com interresfriamento e ciclo por absorção de simples efeito. Os balanços de custo são avaliados em nível dos componentes dos ciclos e os custos exergéticos unitários dos fluxos internos e do produto são obtidos. Também é feito o balanço de exergia e comparado com a diferença entre insumo e produto para cada unidade física dos ciclos, além da avaliação das razões produto-insumo. Os resultados mostram que os custos exergéticos unitários nunca são menores que a unidade e que as razões produto-insumo nunca são maiores que 100%, além da análise exergética gerar os mesmos valores de irreversibilidades que a diferença entre insumo e produto. Por fim, comentários são tecidos, bem como sugestões para trabalhos futuros / The goal of this work is to present an alternative thermoeconomic approach whose application to refrigeration cycles should isolate dissipative components, as condensers and valves, in the productive structure so the yielded results are consistent. The approach, called UFS Model, is based on the concept of physical exergy splitting into three components, namely, internal energy term, flow work term and entropic term and is applied to five refrigeration cycles, namely, Carnot s reverse cycle, vapor-compression simple cycle, vaporcompression cascade cycle, vapor-compression cycle with intercooling and simple-effect absorption cycle. The cost balances are assessed at the components level and the exergetic unit costs of both internal flows and plant product are obtained. Also, the exergy analysis is done and compared with the difference of fuel (or resource) and product of each physical unit, besides the assessment of the product-resource ratios. The results show that the exergetic unit costs are never less than one and the product-resource ratios are never greater than 100%. Besides, the exergy analysis yields same irreversibility values of the difference of resource and product. Finally, some remarks are done as well as suggestions for future works

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.

The current study addresses the stability of shock waves propagating through dissipative media, analogous to both granular media and molecular gases undergoing endothermic reactions. In order to investigate the stability, a simple molecular dynamics model was developed to observe shock waves and their structures with the inclusion of energy dissipation. For this, an Event Driven Molecular Dynamics model was implemented in a 2D environment, where a molecule is represented by a disk. The simulations addressed the formation of a shock wave in a gas by the sudden acceleration of a piston. Inelastic collisions were assumed to occur only if an impact velocity threshold is surpassed, representing the activation energy of the dissipative reactions. Parametric studies were conducted for this molecular model, by varying the strength of the shock wave, the activation threshold and the degree of inelasticity in the collisions. The resulting simulations showed that a shock structure does indeed become unstable with the presence of dissipative collisions. This instability manifests itself in the form of distinctive high density non-uniformities behind the shock wave, which take the form of convective rolls. The spacing and size of this ``finger-like" unstable pattern was shown to be dependent on the degree of inelasticity, the activation energy, and the strength of the driving piston. The mechanism responsible for the instability was addressed by studying the time evolution of the material undergoing the shock wave compression and further relaxation. It is found that the gas develops the instability on the same time scales as the clustering instability in homogeneous gases, first observed by Goldhirsch and Zanetti in granular gases. This confirmed that the clustering instability is the dominant mechanism.

We study two aspects of the problem of a particle moving on a lattice while subject to dissipation, often called the "Schmid model." First, a correspondence between the Schmid model and boundary sine-Gordon field theory is explored, and a new method is applied to the calculation of the partition function for the theory. Second, a traditional condensed matter formulation of the problem in one spatial dimension is extended to the case of an arbitrary two-dimensional Bravais lattice. A well-known mathematical analogy between one-dimensional dissipative quantum mechanics and string theory provides an equivalence between the Schmid model at the critical point and boundary sine-Gordon theory, which describes a free bosonic field subject to periodic interaction on the boundaries. Using the tools of conformal field theory, the partition function is calculated as a function of the temperature and the renormalized coupling constants of the boundary interaction. The method pursues an established technique of introducing an auxiliary free boson, fermionizing the system, and constructing the boundary state in fermion variables. However, a different way of obtaining the fermionic boundary conditions from the bosonic theory leads to an alternative renormalization for the coupling constants that occurs at a more natural level than in the established approach. Recent renormalization group analyses of the extension of the Schmid model to a two-dimensional periodic potential have yielded interesting new structure in the phase diagram for the mobility. We extend a classic one-dimensional, finite temperature calculation to the case of an arbitrary two-dimensional Bravais lattice. The duality between weak-potential and tightbinding lattice limits is reproduced in the two-dimensional case, and a perturbation expansion in the potential strength used to verify the change in the critical dependence of the mobility on the strength of the dissipation. With a triangular lattice the possibility of third order contributions arises, and we obtain some preliminary expressions for their contributions to the mobility.

We study two aspects of the problem of a particle moving on a lattice while subject to dissipation, often called the "Schmid model." First, a correspondence between the Schmid model and boundary sine-Gordon field theory is explored, and a new method is applied to the calculation of the partition function for the theory. Second, a traditional condensed matter formulation of the problem in one spatial dimension is extended to the case of an arbitrary two-dimensional Bravais lattice. A well-known mathematical analogy between one-dimensional dissipative quantum mechanics and string theory provides an equivalence between the Schmid model at the critical point and boundary sine-Gordon theory, which describes a free bosonic field subject to periodic interaction on the boundaries. Using the tools of conformal field theory, the partition function is calculated as a function of the temperature and the renormalized coupling constants of the boundary interaction. The method pursues an established technique of introducing an auxiliary free boson, fermionizing the system, and constructing the boundary state in fermion variables. However, a different way of obtaining the fermionic boundary conditions from the bosonic theory leads to an alternative renormalization for the coupling constants that occurs at a more natural level than in the established approach. Recent renormalization group analyses of the extension of the Schmid model to a two-dimensional periodic potential have yielded interesting new structure in the phase diagram for the mobility. We extend a classic one-dimensional, finite temperature calculation to the case of an arbitrary two-dimensional Bravais lattice. The duality between weak-potential and tightbinding lattice limits is reproduced in the two-dimensional case, and a perturbation expansion in the potential strength used to verify the change in the critical dependence of the mobility on the strength of the dissipation. With a triangular lattice the possibility of third order contributions arises, and we obtain some preliminary expressions for their contributions to the mobility.

<p>Negative differential conductivity (NDC) is a nonlinear property of electronic transport for high electric field strength found in materials and devices such as semiconductor superlattices, bulk GaAs and Gunn diodes. In spatially extended systems, NDC can cause rich dynamics such as static and mobile field domains and moving charge fronts. In this thesis, these phenomena are studied theoretically and numerically for semiconductor superlattices. Two classes of models are considered: a discrete model based on sequential resonant tunneling between neighboring quantum wells is used to described charge transport in weakly-coupled superlattices, and a continuum model based on the miniband transport is used to describe charge transport strongly-coupled superlattices.</p> <p>The superlattice is a spatially extended nonlinear system consisting a periodic arrangement of quantum wells (e.g., GaAs) and barriers (e.g., AlAs). Using a discrete model and only considering one spatial dimension, we find that the boundary condition at the injecting contact has a great influence on the dynamical behavior for both fixed voltage and transient response. Static or moving field domains are usually inevitable in this system. In order to suppress field domains, we add a side shunting layer parallel to the growth direction of the superlattice. In this case, the model includes both vertical and lateral spatial degrees of freedom. We first study a shunted weakly-coupled superlattice for a wide range of material parameters. The field domains are found to be suppressed for superlattices with small lateral size and good connection between the shunt and the quantum wells of the superlattice. As the lateral size of the superlattice increases, the uniform field configuration loses its stability to either static or dynamic field domains, regardless of shunt properties. A lower quality shunt generally leads to regular and chaotic current oscillations and complex spatio-temporal dynamics in the field profile. Bifurcations separating static and dynamic behaviors are characterized and found to be dependent on the shunt properties. Then we adopt the model to study the shunted strongly-coupled superlattice with the continuum model. Key structural parameters associated with both the shunt layer and SL are identified for which the shunt layer stabilizes a uniform electric field profile. These results support the possibility to realize a SL-based THz oscillator with a carefully designed structure.</p> <p>Another important behavior of the static field domains in the weakly-coupled superlattice is bistability, i.e., two possible states (i.e., electric field configurations) for a single voltage. Noise can drive the system from one of these states (the metastable state) to the other one (the globally stable state). The process of escape from the metastable state can be viewed as a stochastic first-passage process in a high-dimensional system that possesses complex stability eigenvalues and for which a global potential energy function does not exist. This process is simulated using a stochastic differential equation system which incorporates shot noise. The mean switching time &tau; is fitted to an exponential expression <italic>e</italic><super>(Vth-V)<super>&alpha;</super>/D</super>, where V_th denotes the voltage at the end of the current branch. The exponent &alpha; in the fitting curve deviates from 1.5 which is predicted for a generic one dimensional system. We develop an algorithm to determine an effective locally valid potential. Principal component analysis is applied to find the most probable path for switching from the metastable current state.</p> / Dissertation