Nesta tese, obtemos estados quânticos que satisfazem a equação de Schrödinger, para Hamiltonianos quadráticos de forma geral e, ao mesmo tempo, permitem de maneira natural obter a correspondência com a descrição clássica. Usamos o método de integrais de movimento para construir operadores de criação e aniquilação, que satisfazem a álgebra de Weyl-Heisenberg. Dessa forma, construímos os estados de número generalizados (ENG) de maneira análoga ao que é feito para os estados de Fock. Obtemos diferentes famílias de estados coerentes (EC), através de uma superposição dos ENG, que chamamos de estados coerentes generalizados (ECG). Esses estados são rotulados pela constante complexa z escrita em termos do valor esperado inicial da coordenada e do momento. Escrevemos os ECG em função do desvio padrão inicial na coordenada, $\\sigma_q$, de modo a minimizar a relação de incerteza de Heisenberg no instante de tempo inicial. Obtemos, de forma pioneira, os ECG para partícula livre e discutimos em detalhes suas propriedades, tal como a relação de completeza, a minimização das relações de incerteza e a evolução da correspondente densidade de probabilidade. Mostramos que o valor esperado da coordenada e do momento segue ao longo da trajetória clássica no espaço de fase. Mostramos que, quando o comprimento de onda da partícula livre é muito menor que $\\sigma_q$, os EC se comportam como estados semiclássicos. Além da partícula livre, construímos pela primeira vez, os ECG para o oscilador invertido e discutimos em detalhes suas propriedades. Mostramos que os ECG de sistemas diferentes podem ser relacionados, impondo condições sobre os parâmetros do Hamiltoniano. Por fim, consideramos Hamiltonianos dependentes do tempo, em particular, construímos os ECG, de forma exata, para um oscilador harmônico cuja frequência varia explicitamente no tempo. Mostramos ainda modelos úteis para obter solução exata de sistemas dependentes do tempo, fazendo analogia com a equação de spin ou equação de Schrödinger unidimensional independente do tempo. Além disso, desenvolvemos um método próprio, que fixa a solução e em seguida determinamos a forma da frequência. / In this thesis we obtain quantum states that satisfy the Schrödinger equation for quadratic Hamiltonians in the general form and at the same time allow, naturally, to obtain the correspondence with the classical description. For this, we use the method of integrals of motion to construct creation and annihilation operators, which satisfy the algebra of Weyl-Heisenberg. Thus, we obtain the generalized number states (GNS) in the same way that is done for the Fock states. We obtain diferent families of coherent states (CS) that we call generalized CS (GCS), by a superposition of GNS. These states are labeled by a complex constant z which is written in terms of the initial expected values of the coordinate and momentum. We write the GCS in terms of the initial standard deviation of the coordinate, $\\sigma_q$, which provides the minimization of Heisenberg uncertainty relation at the initial instant time. In particular, we obtain for the first time the GCS for the free particle and discuss in detail their properties, such as the completeness relation, the minimization of uncertainty relations, and the evolution of the corresponding probability density. We show that the expected values of coordinated and momentum propagate along the classical trajectory in phas espace. When the Compton wavelength is much smaller than $\\sigma_q$, the CS can be considered a semiclassical state. In addition to the free particle, we obtain for the first time the GCS for the inverted oscillator and discuss in detail their properties. We show that the GCS of diferent systems can be related by imposing conditions on the parameters of the Hamiltonian. Finally, we consider the time-dependent Hamiltonian, especially to obtain the GCS for a harmonic oscillator whose frequency varies explicitly in time. We also show useful models to obtain exact solution for time-dependent systems, by analogy with the spin equation or one-dimensionaltime-independent Schrödinger equation, as well as a method which consists first to find the solution and then determine the shape of the frequency.

La propagation des états cohérents est un sujet actif de la recherche de ces dernières décennies. Un état cohérent est la modélisation quantique d'une particule classique. La trajectoire d'une particule chargée dans un champ magnétique fort, i.e. qui ne s'annule pas, est donnée par le mouvement centre guide : il s'agit d'oscillations rapides autour d'un centre virtuel dont la dynamique plus lente suit les lignes de champ magnétique. Le sujet de ma thèse est d'étudier le pendant magnétique de ce résultat. Il est connu que pour des temps courts, c'est à dire bornés en le paramètre semi-classique h, la dynamique d'un état cohérent est donnée par la dynamique classique de la particule associée. Le problème est alors l'étude de la dynamique en temps longs de tels états. Pour des états cohérents de basses énergies, en utilisant des résultats de forme normale et de régularité elliptique magnétique, on prouve le résultat suivant de propagation magnétique en temps longs. Un état cohérent sous un champs magnétique se propage pour des temps de l'ordre de l'inverse de h en une somme d'états cohérents évoluant sur une même trajectoire, mais à des vitesses différentes. / The propagation of coherent states was extensively studied over past decades. A coherent state is the quantum version of a classical particle. The trajectory of a charged particle under strong magnetic field, that is a non-vanishing field, is given by the center guide motion : it is high speeds oscillations around a virtual center that moves slowly along the field lines of the magnetic field. The aim of this thesis is the study of the quantum translation of this. It is well-known that for short times, i.e. bounded times with respect to the semiclassical parameter h, the dynamics of such a state is given by the classical trajectory of the associated particle. The thing is to study the dynamics of coherent states for long times, that are times going to infinite as h goes to 0. For low energy coherent states, using normal form and magnetic elliptical regularity results, we prove the following long time magnetic propagation result. A coherent state under strong magnetic field is propagated as a sum of coherent states following the same dynamics, but with different speeds.

Background Quantifying joint deformity in people with rheumatoid arthritis (RA) and psoriatic arthritis (PsA), using high resolution peripheral quantitative computed tomography (HR-pQCT), remains problematic because it is difficult to estimate where the healthy joint surface would have been. Methods The second metacarpophalangeal of RA, PsA and healthy subjects were imaged with HR-pQCT. Using the bone surfaces of the healthy cohort as a reference, the method predicted the healthy surface of each individual diseased bone surface. Quantifiable outcomes were measured based on differences between the predicted healthy surface and the actual diseased surface. Sensitivity studies were conducted to measure precision, and the algorithm was validated against artificially created deformities with known geometries. Results Subjects with PsA and RA had significantly greater occurrences of erosion based surface outcomes than the healthy cohort. Sensitivity analyses revealed precision errors of up to 0.26 mm. Validating the algorithm showed an average accuracy error of 0.12 mm (4%) for detecting erosions and 0.27 mm (20%) for detecting periosteal bone growths. Conclusions The new method allows for visualization and quantification of surface changes within the affected joint by identifying areas of erosion and periosteal bone formation. Surface based outcomes are a novel way to interpret and further quantify articular bone changes affected by PsA and RA.

Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T17:51:39Z (GMT). No. of bitstreams: 1 Grigolo_Adriano_D.pdf: 6040981 bytes, checksum: 874a21109be77dc3f306ac9ce74f90b5 (MD5) Previous issue date: 2017 / Resumo: Uma versão generalizada do método 'coupled coherent states' é desenvolvida para estados coerentes associados a grupos de Lie arbitrários. Em contraste com a abordagem original, restrita a funções de base gaussianas, o método estendido é adequado para propagação de estados quânticos de sistemas exibindo propriedades físicas destituídas de análogo clássico, tais como graus de liberdade de spin ou indistinguibilidade de partículas. A formulação para o caso de sistemas com um número fixo de partículas idênticas interagentes é examinada em detalhe, sendo este um caso relevante descrito em termos de estados coerentes do grupo especial unitário. A técnica é ilustrada com aplicações simples, envolvendo modelos de Hubbard bosônicos e fermiônicos. Diversos aspectos da implementação numérica são discutidos / Abstract: A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original approach, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring non-classical physical properties, such as spin degrees of freedom or particle interchange symmetry. The formulation for the relevant case of number-conserving systems of interacting identical particles, most adequately described in terms of coherent states of the special unitary group, is studied in detail. The technique is illustrated with applications to simple Hubbard-like models for both bosons and fermions. Several aspects of the numerical implementation are discussed / Doutorado / Física / Doutor em Ciências / 2011/20065-4 / 141338/2011-3 / FAPESP / CNPQ

Les propriétés intrinsèques des fibres amplificatrices telles que leur robustesse, leur efficacité, leur qualité de faisceau ou encore leur compacité ou leur bonne gestion thermique, en font un candidat idéal pour le développement de sources lasers de haute puissance, capables de rivaliser aujourd’hui avec les lasers solides. Les applications de ces sources avec de fortes puissances sont nombreuses : l’industrie (usinage, marquage), la défense (télémétrie, imagerie), la physique des particules. Dans ce dernier cas, des sources ultra-brèves et ultra-intenses permettent d’envisager de nouvelles applications telles que la proton-thérapie ou bien le remplacement des synchrotrons actuels par des architectures moins encombrantes et ayant un rendement plus important. Ce travail de thèse s’est déroulé dans le contexte du projet ICAN qui vise à étudier l’architecture de ces nouvelles sources.La combinaison cohérente de plusieurs amplificateurs fibrés en parallèle permet d’augmenter la puissance de ces sources. Pour atteindre les énergies visées dans le projet ICAN, la combinaison cohérente de 10 000 fibres doit être envisagée. L’objectif de cette thèse est de développer des techniques de contrôle de la phase compatibles avec un très grand nombre de fibres, pour leur application aux lasers ultra-intenses nécessaires à la physique des particules.Deux architectures de combinaison cohérente basées sur une mesure de phase interférométrique ont été réalisées dans cette thèse. La première, basé sur l’holographie numérique, permet un contrôle de la phase sans aucun calcul, collectif tant au niveau de la mesure que de la correction. La seconde architecture possède un contrôle actif de phase basé sur un algorithme de traitement d’images et elle a une bande passante compatible avec le spectre de bruit des amplificateurs. La combinaison cohérente de 16 fibres à 1kHz avec une erreur résiduelle de phase de λ/60mrs a été démontrée. La compatibilité de ces deux architectures avec 10 000 fibres a été étudiée et nous avons apporté quelques éléments pour la combinaison cohérente d’un très grand nombre de fibres. / The intrinsic properties of optical fibers like robustness, efficiency, beam quality, compactness and good thermal management can now compete with solid state lasers to develop high power laser sources. The applications of such sources include industry (machining, marking), defense (telemetry, lidar), and fundamental research. In this case, high intensity lasers are compulsory to produce the next generation of particles accelerators more efficient and more compact, both for fundamental research and its direct applications such as proton therapy. This work was done in the context of the ICAN project, which studies the feasibility of such sources.To overcome the limitations in terms of power of a single amplified fiber, an idea is to use several fiber lasers and to combine them coherently. To reach the ultra-high peak power and high average power requirements for these applications, the coherent beam combining of 10,000 fiber amplifiers has to be envisaged. The goal of the work is to develop a scheme of phase control scalable to a high number of combined fibers.Two schemes based on an interferometric phase measurement are realized in this work. The fist scheme, based on digital holography, permits a collective phase measurement and correction without calculation. The second scheme is based on an active phase control with individual phase modulators. This control requires an image processing algorithm and has a bandwidth compatible with the phase spectral noise of the amplifiers. The coherent combining of 16 fibers at 1kHz with a residual phase shift error of λ/60rms is achieved in this case. We use this second scheme to evaluate its scalability. We show that the coherent combining of 10,000 fibers using off-the-shelf components is already possible.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Sun Tong Lau. / M.S.

A eletrodinâmica clássica estocástica pode ser entendida como sendo a teoria clássica de Maxwell, onde se inclui um novo elemento da realidade física: As flutuações eletromagnéticas de ponto zero. Sob esse enfoque, estudamos a interação de um \"ensemble\", de osciladores harmônicos carregados com a radiação térmica e de ponto zero (atérmica). Incluímos os efeitos de dissipação através da força de reação da radiação. Além disso estudamos também a excitação do oscilador por uma força determinística com dependência temporal arbitrária. Nossa análise estatística do sistema físico é baseada na solução exata da equação de Fokker-Planck adequada ao problema. Obtém-se a evolução temporal, no espaço de fase, para uma dada distribuição inicial que caracteriza um \"ensemble\" de osciladores forçados que apresentam estados excitados na forma de estados coerentes e estados coerentes comprimidos e pulsantes. A comparação direta com a formulação quântica do mesmo problema nos faz reconhecer que é possível obter da física clássica alguns resultados antes só obtidos pela teoria quântica. Identificamos na radiação de ponto zero o ingrediente que torna possível entender a estabilidade do estado fundamental e o princípio de incerteza. / Classical stochastic electrodynamics may be understood as classical electrodynamics theory, when a new element of physical reality is included: The zero point electrodynamics fluctuations. Under this approach, we study the interaction of a charged harmonic oscillator with the thermal radiation and zero point radiation. We include the effect of dissipation by the radiation reaction force. We also study the excitation of this oscillator by a deterministic force with arbitrary temporal dependence. Our statistical analysis of the physical system is based on the exact solution of the appropriate Fokker-Planck equation. We get the temporal evolution in phase space for a given initial distribution that characterizes one \"ensemble\" of forced oscillators that presents excited states in the coherent and squeezed states form. A direct comparison with the quantum formulation of the same problem make us recognize that it is possible to get some results from classical physics which were accomplished previously only by quantum theory. We identify in the zero point radiation the ingredient that makes it possible to understand the stability of the fundamental state and the uncertainty principle.

L'imagerie par diffraction des rayons X coh´erents (CDI) en condition de Bragg est utilis´e pour ´etudier la d´eformation de nano-objets uniques. Ceci est possible grˆace au d´eveloppement d'optique focalisante, comme les lentilles de Fresnel (FZP), produisant un faisceau sub-micronique coh´erent. Les nanostructure ´etudi´ees sont reconstruite avec des algorithmes d'inversion `a partir de donn´ees de diffraction, sous la forme d'un objet complexe, o`u l'amplitude correspond `a la densit´e ´electronique 3D et la phase correspond `a la projection de la d´eformation de l'objet (par rapport `a un r´eseau cristallin parfait) dans la direction du vecteur de diffraction. Dans ce travail, nous avons ´etudi´e la d´eformation dans des nanofils h´et´erognes (nanofil de GaAs avec une mono-couche de boˆıtes quantiques de InAs) et homog`enes (silicium fortement contraint sur isolant (sSOI)). Lorsqu'un faisceau focalis´e de rayons X est utilis´e, `a la fois l'amplitude et la phase de l'onde incidente doivent ˆetre connu pour une ´etude quantitative. Le faisceau focalis´e utilis´e pendant les exp´eriences a ´et´e recontruit avec la technique CDI, et les effets de cette fonction d'illumination sur l'imagerie de nanofils contraints ont ´et´e ´etudi´es. Mots-cl´es: Imagerie par diffraction x coh´erente, contrainte, nanofils, algorithms d'inversion / The coherent diffraction imaging technique (CDI) in Bragg condition can be used to study strain in single nanowires. This is possible due to the recent development of dedicated focusing optics, e.g. Fresnel Zone Plate (FZP), offering the possibility of focusing x-ray beams to sub-micron sizes while preserving a coherent beam. This technique allows to reconstruct (using phase retrieval algorithms) the studied nanostructure as a complex-valued density map, where the amplitude corresponds to the electronic density and the phase to the displacement of the atoms with respect to a perfect crystalline lattice projected onto the scattering vector. The application of CDI to image the strain into heterogeneous (GaAs nanowire with an insertion of 1 monolayer of quantum dots and InSb nanowire with and insertion of InP) and homogeneous highly stressed nano-structures (strained Silicon-on-Insulator lines) has been studied in this work. When using focused X-ray beams, both the amplitude and of the incoming wavefield must be known for a quantitative reconstruction. CDI has been used to reconstruct the coherent wavefield used during experiments and the effects of this illumination function for the imaging of strained nanowires have been also studied. Keywords: Coherent X-ray diffraction imaging, strain, nanowires, phase retrieval algorithm

New quantitative methods are developed for analyser-based phase contrast imaging (ABI) with hard X-rays. In the first instance we show that quantitative ABI may be implemented using an extended incoherent source. Next, we outline how complex Green’s functions may be reconstructed from phase contrast images and we apply this method to reconstruct the thick perfect crystal Green’s function associated with an ABI imaging system. The use of quantitative ABI with incoherent X-ray sources is not widespread and the first set of results pertains to the feasibility of quantitative ABI imaging and phase retrieval using a rotating anode X-ray source. The necessary conditions for observation of ABI phase contrast are deduced from elementary coherence considerations and numerical simulations. We then focus on the problem of extracting quantitative information from ABI images recorded using an extended incoherent X-ray source. The results of an experiment performed at Friedrich-Schiller University, Germany using a rotating anode X-ray source demonstrate the validity of our approach. It is shown that quantitative information may be extracted from such images under quite general and practicable conditions. We then develop a new use for phase contrast imaging systems that allows the Green’s function associated with a linear shift-invariant imaging system to be deduced from two phase contrast images of a known weak object. This new approach is applied to X-ray crystallography where the development of efficient methods of inferring the phase of rocking curves is an important open problem. We show how the complex Green’s function describing Bragg reflection of a coherent scalar X-ray wavefield from a crystal may be recovered from a single image over a wide range of reciprocal space simultaneously. The solution we derive is fast, non-iterative and deterministic. When applied to crystalline structures for which the kinematic scattering approximation is valid, such as thin crystalline films, our technique is shown to solve the famous one-dimensional phase retrieval problem which allows us to directly invert the Green’s function to retrieve the depth-dependent interplanar spacing. Finally we implement our Green’s function retrieval method on experimental data collected at the SPring-8 synchrotron in Hyogo, Japan. In the experiment we recorded analyser-based phase contrast images of a known weak object using a thick perfect silicon analyser crystal. It is then demonstrated that these measurements can be inverted to recover the complex Green’s function associated with the analyser crystal Bragg peak. The reconstructed Green’s function is found to be in good agreement with the prediction of dynamical diffraction theory.

Coherent detection employing multilevel modulation formats has become one of the most promising technologies for next generation high speed transmission systems due to the high power and spectral efficiencies. Using the powerful digital signal processing (DSP), coherent optical receivers allow the significant equalization of chromatic dispersion (CD), polarization mode dispersion (PMD), phase noise (PN) and nonlinear effects in the electrical domain. Recently, the realizations of these DSP algorithms for mitigating the channel distortions in the coherent transmission systems are the most attractive investigations. The CD equalization can be performed by the digital filters developed in the time and the frequency domain, which can suppress the fiber dispersion effectively. The PMD compensation is usually performed in the time domain with the adaptive least mean square (LMS) and constant modulus algorithms (CMA) equalization. Feed-forward and feed-back carrier phase estimation (CPE) algorithms are employed to mitigate the phase noise (PN) from the transmitter (TX) and the local oscillator (LO) lasers. The fiber nonlinearities are compensated by using the digital backward propagation methods based on solving the nonlinear Schrödinger (NLS) equation and the Manakov equation. In this dissertation, we present a comparative analysis of three digital filters for chromatic dispersion compensation, a comparative evaluation of different carrier phase estimation methods considering digital equalization enhanced phase noise (EEPN) and a brief discussion for PMD adaptive equalization. To implement these investigations, a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying (NRZ-PDM-QPSK) coherent transmission system with post-compensation of dispersion is realized in the VPI simulation platform. In the coherent transmission system, these CD equalizers have been compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations and their computational complexity. The carrier phase estimation using the one-tap normalized LMS (NLMS) filter, the differential detection, the block-average (BA) algorithm and the Viterbi-Viterbi (VV) algorithm is evaluated, and the analytical predictions are compared to the numerical simulations. Meanwhile, the phase noise mitigation using the radio frequency (RF) pilot tone is also investigated in a 56-Gbit/s NRZ single polarization QPSK (NRZ-SP-QPSK) coherent transmission system with post-compensation of chromatic dispersion. Besides, a 56-Gbit/s NRZ-SP-QPSK coherent transmission system with CD pre-distortion is also implemented to analyze the influence of equalization enhanced phase noise in more detail. / QC 20120528