The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.

The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular,<br />a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.

Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.

Utilizamos um formalismo de operadores e a técnica de grupo de renormalizacao de Dasgupta, Ma e Hu para analisar o efeito de distribuições inomogêneas dos parâmetros sobre o comportamento crítico de um modelo estocástico simples. O processo de contato em uma dimensão constitui talvez o modelo mais simples que apresenta uma transição de fase para um estado absorvente. Nós usamos as seqüências de Fibonacci, duplicação de período e triplicação de período para introduzir inomogeneidades aperiódicas no processo de contato unidimensional e em uma cadeia quântica de spin. Usando procedimento de grupo de renormalização de desordem forte, estabelecemos algumas relações entre propriedades dos operadores renormalizados e grandezas termodinâmicas ou médias. Fomos capazes de testar o critério de relevância de flutuações geométricas de Harris-Luck, de obter vários expoentes críticos, e de observar aspectos característicos de dinâmica lenta e oscilações log-periódicas. A sequência de triplicação de período nos leva aos expoentes = ln (7/9)/ ln (4/9), = ln (9/7)/ ln 4, = ln 3/ ln (3/2) e k = ln 2/ ln (3/2). Usamos técnicas de Monte Carlo para confirmar os resultados de grupo de renormalização. As simulações numéricas indicam a validade do critério de relevância de Harris-Luck, e corroboram o caráter universal do comportamento crítico desses sistemas aperiódicos. / We use an operator formalism and the renormalization-group technique of Dasgupta, Ma and Hu to analyze the effects of a nonhomogeneous distribution of parameters on the critical behavior of simple stochastic model system. The contact process in one dimension is perhaps the simplest model to display a phase transition to an absorbing stationary state. We use the Fibonacci, period-doubling and period-tripling sequences for introducing aperiodic inhomogeneities in the one dimensional contact process and in a quantum Ising chain. Using strong-disorder renormalization-group procedures, we establish some relations between properties of renormalized operator and of thermodynamic or mean quantities. We were able to test a well-known criterion of relevance of geometric fluctuations, to obtain a number of critical exponents, and to point out features of slow-dynamics and log-periodic oscillations. The period-tripling sequence leads to the critical exponents = ln (7/9)/ ln (4/9), = ln (9/7)/ ln 4, = ln 3/ ln (3/2) and k = ln 2/ ln (3/2). We then used Monte Carlo techniques to check renormalization-group results. The numerical simulations indicate the validity of the Harris-Luck criterion of relevance of the geometric fluctuations, and generally support the universal character of the critical behavior of these aperiodic systems.

Networked control over wireless sensor and actuator systems is of growing importancein many application domains. Energy and communication bandwidth are scarce resources in such systems. Despite that feedback control might only be needed occasionally, sensor and actuator communications are often periodic and with high frequency in today’s implementations. In this thesis, resource-constrained wireless networked control systems with an adaptive sampling period are considered. Our first contribution is a system architecture for aperiodic wireless networked control. As the underlying data transmission is performed over a shared wireless network, we identify scheduling policies and medium access controls that allow for an efficient implementation of sensor communication. We experimentally validate three proposed mechanisms and show that best performance is obtained by a hybrid scheme, combining the advantages of event- and self-triggered control as well as the possibilities provided by contention-based and contention-free medium accesscontrol. In the second contribution, we propose an event-triggered PI controller for wireless process control systems. A novel triggering mechanism which decides the transmission instants based on an estimate of the control signal is proposed. It addresses some side-effects that have been discovered in previous PI proposals, which trigger on the state of the process. Through simulations we demonstrate that the new PI controller provides setpoint tracking and disturbance rejection close to a periodic PI controller, while reducing the required network resources. The third contribution proposes a co-design of feedback controllers and wireless medium access. The co-design is formulated as a constrained optimization problem, whereby the objective function is the energy consumption of the network and the constraints are the packet loss probability and delay, which are derived from the performance requirements of the control systems. The design framework is illustrated in a numerical example. / QC 20111004

Radio frequency interference is an ever growing problem in the wireless community. This dissertation presents methods to reduce interference for vehicular multi-antenna devices. This document is organized into two parts: the main chapters and the appendices. The main chapters present research conducted primarily by the author. These deserve the reader's primary attention. The appendices showcase contributions made by the author serving in a supporting role to projects led by others and/or do not fit the vehicular theme. These should receive secondary attention. The main chapter contributions are summarized as follows. A device was created that provides over 105 dB of transmit to receive isolation in a full duplex printed circuit board radio. This technology can improve the effective range of vehicular radar systems and increase the bandwidth of full duplex communication schemes for vehicles. The technologies involved are compatible with existing circuit board topologies and are mindful of the size and weight requirements for vehicular use. This isolation performance pushes the state of the art for printed circuit board designs and provides greater capability for these kinds of devices. Recent system on chip computing architectures are opening new pathways for integrating phased array technologies into a single chip. The computer engineering required to configure these devices is beyond the capabilities of many vehicle systems engineers, inviting the author to use one to implement a 16 antenna adaptive beamformer for GPS. The adaptive beamformer can combat multipath bounces and malicious spoofing from ground sources. The high rate analog conversion architecture eliminates the local oscillator distribution to simplify the analog front end to an active antenna. This allows vehicular phased arrays to use smaller footprints and suggests that multi-antenna beamforming devices may be easier to deploy on small to midsized vehicles. Bench tests of the beamformer indicate it can adapt to the environment and increase the received signal strength suggesting it can improve GPS quality for active deployments. The bank of subspace projection beamformers is a popular choice for mitigating interference in digital phased array receivers. A method was discovered that maps that matrix operator into a circuit topology that is simple to implement in an analog circuit and cancels across the entire bandwidth simultaneously. This can offload computational interference mitigation from the signal processor while still allowing secondary multi-pixel digital beamforming downstream. This beamformer was analytically connected to the body of phased array literature and studied to estimate practical error bounds and design methods of calibration.

<p dir="ltr"> Nowadays, inkjet printers are widely used all around the world. But how do they transfer the digital image to a map that can control nozzle firing? In this preliminary report, we briefly illustrate that part of the printing pipeline that starts from a halftone image and ends with Hardware Ready Bits (HRBs). We also describe the implementation of the multi-pass printing method with a designed print mask. HRBs are used to read an input halftone CMY image and output a binary map of each color to decide whether or not to eject the corresponding coloranr drop at each pixel position. In general, for an inkjet printer, each row of the image corresponds to one specific nozzle in each swath so that each swath will be the height of the printhead \cite{torpey1997multipass}. To avoid visible white streaks due to clogged or burned out color nozzles, the method called multi-pass printing is implemented. Subsequently, the print mask is introduced so that we can decide during which pass each pixel should be printed. Once we figure out how to transfer the digital image to our printing signals. We start to think about improving the color performance for the inkjet printer. In one of our previous papers \cite{wang2020developing}, we described the color management pipeline that was applied to our nail inkjet printer, which is used to map the source gamut to the destination printer gamut. However, the resulting prints are not as vivid as we would like to have, since those prints are not well saturated. To obtain more saturated prints, we propose a saturation enhancement method based on image segmentation and hue angle. This method will not necessarily give us the closest representation of the colors within the input image but could give us more saturated prints. The main idea of our saturation enhancement method is to keep the lightness and hue constant, while stretching the chroma component.</p><p><br></p><p dir="ltr"> In one of our previous papers \cite{hu2021improving}, we mostly focused on the color saturation problem in our inkjet printer. However, our partner reported that there are some boundary noise pixels on the background, which are quite visible when the background is white. By checking the pipeline of our printing procedure, we realized that the noise stray dots are generated during the halftoning procedure. This part of the dissertation is dedicated to separating the white background from the foreground, which enables us to constrain the error diffusion process inside the white background. The main idea is to apply image segmentation, which could help us to precisely extract the background.</p><p><br></p><p dir="ltr"> Lastly, inspired by the paper \cite{smith2023chiral}, we decided to design an aperiodic clustered-dot screen, which may have better performance compared to the current DBS screen. This screen generation method is offline, so the time cost is not our main consideration. The output halftone result is what we concentrate on. This screen is generated based on a polygon shape, which is called tile(1,1) defined by the paper \cite{smith2023chiral}. We keep extending this single polygon shape to obtain the combination aperiodic shape that is called a supertile. After obtaining the final supertile, we assigned each tile(1,1) shape to either a dot or a hole based on the complementary symmetry property. Finally, based on some interpolation methods, we generate the threshold matrix. </p>

Neste trabalho realizo uma adaptação do método de Ma, Dasgupta e Hu para o estudo e caracterização das transições de fase quânticas, induzidas por um campo transverso, em cadeias XY de spins 1/2, unidimensionais e aperiódicas, no espírito da adaptação correspondente para cadeias XXZ. O presente trabalho determina de forma analítica uma série de expoentes críticos associados às transições ferro-paramagnéticas do sistema, e dá pistas quanto à natureza das estruturas presentes no estado fundamental. Os resultados são então testados pelo emprego da técnica de férmions livres, da análise de nite size scaling e, no limite de Ising, de resultados extraídos do mapeamento do problema em uma caminhada aleatória. / We employ an adaptation of the Ma, Dasgupta, Hu method in order to analyze the quantum phase transition, induced by a transversal magnetic eld, at spin-1/2 aperiodic XY chains, in analogy to the corresponding adaptation for XXZ chains. We derive analytical expressions for some cri tical exponents related with the ferro-paramagnetic transitions, and shed light onto the nature of the ground state structures. The main results obtained by this approach were tested by the free-fermion method, nite-size scaling analyses and, at the Ising limit of the model, by using results derived from a mapping to a random-walk problem.

Dans le cadre de ses recherches menées sur la fusion par confinement inertiel, le Commissariat à l’énergie atomique et aux énergies alternatives met en œuvre un spectromètre X large bande étalonné en absolu et résolu en temps, appelé Diagnostic de Mesure du rayonnement X. Ce diagnostic, composé de 20 voies de mesure, permet de mesurer l’émissivité spectrale d’un plasma créé par laser entre 50 eV et 20 keV. Nous avons développé des voies de mesure complémentaires aux voies existantes, afin d’obtenir une redondance et une amélioration de la précision de la mesure. Le principe de ces nouvelles voies de mesure repose sur un concept original permettant d’obtenir des fonctions de transfert spectrales bornées et constantes. Deux voies ont été développées pour les gammes spectrales 2 – 4 keV et 4 – 6 keV, utilisant des miroirs multicouches apériodiques réalisés au Laboratoire Charles Fabry en Cr/Sc et Ni/W/SiC/W, respectivement. Ces miroirs ont ensuite été caractérisés sur synchrotrons puis intégrés dans le spectromètre. Les nouvelles voies ont été utilisées durant des campagnes d’expériences laser-Plasma sur l’installation laser OMEGA à Rochester (États-Unis). Elles ont permis de déterminer la puissance rayonnée directement avec une seule voie de mesure par bande spectrale et avec une meilleure précision qu’avec celles utilisées habituellement. Les résultats, en bon accord avec les voies de mesure classiques, permettent de valider l’utilisation des miroirs multicouches apériodiques pour la spectrométrie X large bande. / Within the framework of the research on inertial confinement fusion, the “Commissariat à l’énergie atomique et aux énergies alternatives” has studied and implemented an absolute calibrated time-Resolved broadband soft x-Ray spectrometer, called “Diagnostic de Mesure du rayonnement X”. This diagnostic, composed of 20 measurement channels, measures the emitted radiant power from a laser created plasma in the range from 50 eV to 20 keV. We have developed additional measurement channels to obtain redundancy and an improvement in measurement accuracy. The principle of these new channels is based on an original concept to obtain spectral bounded flat-Responses. Two channels have been developed for the 2 – 4 keV and 4 – 6 keV spectral ranges, using aperiodic multilayer mirrors made at the “Laboratoire Charles Fabry” with Cr/Sc and Ni/W/SiC/W layers respectively. These mirrors were characterized at synchrotron radiation facilities and integrated into the spectrometer. The two new channels were used during laser-Plasma experimental campaigns at the OMEGA laser facility in Rochester (USA). This allowed us to determine directly the radiant power with only one measurement within a certain spectral band, and with a better precision when compared with using standard channels. The results, in good agreement with the standard measurement channels, allowed us to validate the use of aperiodic multilayer mirrors for X-Ray broadband spectrometry.

Les centres de rayonnement synchrotron et les Lasers à Électrons Libres (LEL) sont des sources de rayonnement utilisant des Électrons relativistes. Les onduleurs en constituent un élément important : ces instruments qui génèrent un champ magnétique périodique le long de la trajectoire des électrons, guident ces derniers de façon à les faire rayonner ou à rendre l’onde lumineuse émise plus intense. Ce travail porte sur l’étude d’onduleurs de différents types appliqués au Synchrotron SOLEIL, et sur leur possible application sur un LEL. Une première partie du travail porte sur la réalisation pour SOLEIL de deux onduleurs de type APPLE-II. Ce type d’onduleurs permet d’émettre du rayonnement de polarisation variable et les deux onduleurs construits présentent certaines spécificités par rapport à la plupart des onduleurs de ce type. Le premier (HU36) génère un champ magnétique de courte période tout en conservant une valeur crête relativement importante, ce qui lui permet de rayonner sur une large gamme spectrale. Ces caractéristiques entrainent cependant une hystérésis expliquée par la déformation des supports. Les moyens mis en œuvre pour atteindre ces caractéristiques magnétiques et pour réduire l’hystérésis sont présentés. Le deuxième onduleur APPLE-II construit (HU64) présente la double particularité d’être quasipériodique (ou apériodique) afin de réduire la pollution rayonnée aux harmoniques de la longueur d’onde fondamentale, et de permettre l’accès à de la polarisation linéaire inclinée sur une plage de 180° grâce à son châssis étendu. L’optimisation magnétique de sa structure apériodique est détaillée et les difficultés découlant des configurations étendues sont expliquées. Dans un deuxième temps, la réalisation pour SOLEIL d’un troisième onduleur d’un tout autre type est présentée. Il s’agit d’un onduleur hybride sous-vide appelé U20. Des pôles intercalés entre les aimants guident les lignes de champ de façon à augmenter la densité de flux magnétique sur axe, et l’assemblage magnétique ainsi obtenu est installé dans la chambre à vide, ce qui permet de réduire l’entrefer minimum à 5.5 mm et donc, d’accroitre considérablement la valeur crête du champ magnétique généré. Compte-tenu des connaissances acquises pendant la construction des deux onduleurs APPLE-II et de l’onduleur sous-vide, l’étude d’un onduleur combinant ces deux aspects est ensuite proposée. Cet onduleur de tyoe « APPLE-II sous-vide » serait extrêmement polyvalent puisqu’il permettrait l’émission de rayonnement de différentes polarisations sur une large gamme spectrale. L’étude de principe menée ici met en évidence les nombreuses difficultés à surmonter et propose différentes solutions. La dernière partie du travail porte sur l’étude de l’interaction qui s’opère dans le cas d’un LEL au sein de l’onduleur entre les électrons et l’onde lumineuse, conduisant à l’amplification de cette dernière. Des expériences menées en configuration SASE et en mode injecté sur le SPARC (Italie, Frascati) sont rapportées, puis des calculs sont réalisés dans le cadre du projet LUNEX5, pour évaluer l’efficacité de cette interaction dans un onduleur apériodique, et dans l’onduleur APPLE-II sous-vide envisagé précédemment. / Storage rings and Free Electron Lasers (FEL) are relativistic electron based radiation sources, in which an important element is a device called undulator. This apparatus generates a periodic magnetic field along the electron trajectory, guiding the particles in such a way that they lose energy to the benefit of the radiation. This work deals with the study of several undulators of different types, and also their application on FEL sources. A first part of the work is dedicated to the construction of two APPLE-II type undulators for SOLEIL. Undulators of this type are able to emit radiation of variable polarization states, and the two studied devices present some special characteristics with respect to most of APPLE-II undulators. The first one (HU36) generates a short period high value magnetic field, leading to radiation emitted on a large spectral range. These parameters brought about a hysteresis explained by the deformation of the magnet supports, which was reduced. The second APPLE-II undulator (HU64) is characterized by two particularities: its field is quasi-periodic (or aperiodic) in order to reduce the pollution emitted at harmonics of the fundamental wavelength, and it is based on a special frame enabling radiation of tilted linear polarization on the full range of 180°. The optimization of the aperiodic structure is detailed and the difficulties brought about by the extended frame are explained. The third undulator built for SOLEIL is a hybrid in-vacuum one. Ferromagnetic poles guide the magnetic flux lines in order to increase the on-axis flux density, and the magnetic part of the undulator is included inside the vacuum chamber, which leads to a higher value of the generated field. Starting from the knowledge of both APPLE-II and in-vacuum undulators, the study of a device combining both characteristics is then proposed. Such an in-vacuum APPLE-II undulator would consist in a very performant and flexible apparatus because it could emit radiation of variable polarization on a large spectral range. The study points out the technical difficulties and suggests some solutions. The last part of the work deals with the study of the interaction realized in a FEL between electrons and radiation, resulting in the amplification of the light. Experiments performed in both SASE and injected configurations at the FEL SPARC (Italy, Frascati) are reported. Then calculations are made in the case of the FEL French project LUNEX5 to estimate the interaction efficiency when realized inside a quasi-periodic undulator and also through the previously studied in-vacuum APPLE-II one.