<p>Topological materials have been under intense investigation for more than 30 years and have experienced astonishing growth  over the last decade. The two-dimensional electron gas has long served as a model system for the exploration of topological physics, supporting a diverse array of strongly correlated emergent phenomena. Indeed, some of the most stunning topological phases in condensed matter systems are the integer and fractional quantum Hall states forming in two-dimensional electron gases.</p> <p>It was realized early on that electron localization in the bulk has an important role in attaining topological phases, where the sample bulk is well described by randomly localized electrons, known as the Anderson insulator. However, a different type of topological phases forms when charge carriers order in the bulk. Such a charge ordering can only occur in the presence of strong electron-electron interactions and low disorder. Localization of this kind is of a collective nature and differs fundamentally from the single particle physics of the Anderson insulator. The nature of charge ordering, however, is more nuanced than first thought. Indeed, in high Landau levels, Hartree-Fock theories predict the proliferation of numerous exotic bulk insulators, where in the limit of no disorder electrons cluster together and form a hexagonal lattice. Initial observations of these highly correlated insulating phases were limited to low disorder two-dimensional electron gases confined to GaAs/AlGaAs heterostructures. However, recent discoveries of charge ordering in two-dimensional electron gases confined to graphene highlight the universality of this phenomena, irrespective of host material. While progress has been made in understanding the collective insulators residing within integer quantum Hall plateaus, many aspects remain unresolved. In this Dissertation, I discuss the transport properties and energetics of collective insulators forming near integer quantum Hall plateaus in the latest generation of very low disorder two-dimensional electron gases.</p> <p>In chapter  1  I briefly introduce recent developments in our current understanding of the integer quantum Hall effect, where the topological phase is described by both a topological invariant as well as a local order parameter related to the Landau symmetry breaking paradigm. Next, I introduce the basic principles of two-dimensional electron gases confined to semiconductor heterostructures and provide a short summary of recent technological breakthroughs in molecular beam epitaxial growth protocols. The chapter concludes with an introduction to the essential physics of both the integer and the fractional quantum Hall effect.</p> <p>Chapter  2  contains a brief review of the existing literature on the collective insulators forming in sufficiently low disorder two-dimensional electron gases. The primary focus of chapter  2  is on the unique magnetotransport patterns seen at various Landau level filling factors, which support the collective insulator  interpretation. Throughout this chapter I tend to lean on theoretical models that describe these collective phases through the lens of the Hartree-Fock theory; however, it is important to note that both density matrix renormalization group theories and direct diagonalization of small electron systems reach similar conclusions.</p> <p>In chapter  3  I present our data displaying the hallmark transport signatures of a collective insulator residing within the flanks of the nu = 1 integer quantum Hall plateau. Our sample belongs to the latest generation of low disorder 2DEGs confined to GaAs/AlGaAs. I provide a detailed analysis of its development in both temperature and filling factor. The distinct transport signatures we observe strongly overlap in filling factor with prior microwave resonance, surface acoustic wave, compressibility, and tunneling measurements, all of which point to the formation of a collective insulator known as the integer quantum Hall Wigner solid. One puzzling aspect, however, is that while the latter measurements exhibit the integer quantum Hall Wigner solid in older generation samples, transport signatures of this phase appear to be present only in the newest and highest mobility samples. By using distinct features in the magnetoresistance, I propose a stability diagram of the integer quantum Hall Wigner solid in nu −T phase space. Analysis of magnetoresistance profiles at fixed filling factors display sharp peaks within the region of integer quantum Hall Wigner solid phase. It is believed that these sharp peaks are a shared property of collective insulators forming in low disorder two-dimensional electron gases and signal the onset of the electron solid formation. Additional analysis of the magnetoresistance profiles suggests activated transport behavior with a gap energy comparable to that of the plateau center. Lastly, I present large signal measurements of the nu = 1 integer quantum Hall Wigner solid. The data displays strong non-linear behavior in the current-voltage characteristics consistent with the depinning and sliding conduction. However, similar threshold conduction is also seen in the current-voltage characteristics near the center of the integer quantum Hall plateau, where the bulk is an Anderson insulator. Much to our surprise, trends in the threshold current are monotonic in filling factor.</p> <p>In chapter  4  I report on the recent emergence of a newly observed collective insulator residing within the nu = 2 integer quantum Hall plateau and centered at filling factor nu = 1.79. Based on the range of filling factors which stabilizes this collective insulator, we find it distinct from the aforementioned integer quantum Hall Wigner solid. Indeed, the transport behavior is eerily reminiscent to the reentrant insulating phase seen at low filling factors between 1/5 < nu < 2/9. Hence, we term this collective insulator the reentrant integer quantum Hall Wigner solid. Evoking concepts of particle-hole symmetry, we find the reentrant integer quantum Hall Wigner solid to be one member of the larger family of Wigner solids, which is intimately linked through this fundamental symmetry of the system.</p> <p>Lastly in chapter  5 , I explore the energetics of the collective insulators which develop in the N = 2 and N = 3 Landau level, specifically the two- and three-electron bubble phase. We extract the onset temperatures of these exotic bulk insulators from the sharp peaks in the magnetoresistance at fixed filling factor. We compare our measured onset energies with the cohesive energies found from numerical calculations. We find the onset temperatures for the both two- and three-electron bubble phase show an approximately linear trend in filling factor within a single Landau level. In addition, we observe that the three-electron bubble phase has a larger onset temperature than the two-electron bubble phase, a result which is inconsistent with some numerical energy calculations. Thus, our measurements of bubble phase energetics call attention to the importance of the short-range Coulomb interaction in the formation of multi-electron bubble phases and is expected to serve as guide towards the refinement of existing theoretical models.</p>

no / Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group Z(p) and momenta in the group Q(p)/Z(p), and a quantum system with positions in the profinite group (Z) over cap and momenta in the group Q/Z. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T-0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T-0-topologies, in a quantum mechanical context, is discussed.

Yes / An analytic representation with Theta functions on a torus, for systems with variables in ℤ(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied.

Quando um sistema quântico é acoplado à diversos banhos térmicos de diferentes temperaturas, eventualmente um estado estacionário fora do equilíbrio (NESS), caracterizado por correntes internas de calor é atingido. Por um lado, essas correntes são responsáveis por causar decoerência e produzir entropia no sistema. Entretanto, sua existência também induz correlações entre diferentes partes do sistema. Neste trabalho, nós exploramos este duplo aspecto dos NESSs. Usando técnicas do espaço de fase nós calculamos a produção de entropia de Wigner em redes lineares harmônicas. Trabalhando no célebre limite de fraco acoplamento interno e dissipativo, nós obtivemos expressões simples e frechadas para a contribuição de cada corrente de quasi-probabilidade na entropia. Nossa análise também mostra que, a dinâmica interna (reversével) é exclusivamente responsável em manter a produção de entropia (irreversível) estacionária. Considerando um ponto de vista informacional, nós trabalhamos no problema de como quantificar a informação compartilhada entre partes desconexas de uma cadeia quântica em um estado estacionário fora do equilíbrio. Nós mostramos então que esta é mais precisamente caracterizada utilizando a informação mútua condicional (CMI), um quantificador mais geral de correlações tripartites do que a usual informação mútua. Como aplicação, nós utilizamos o paradigmático problema da transferência de energia em uma cadeia de osciladores sujeita a banhos internos auto-consistentes, que podem ser usados para mudar de um transporte balístico para difusivo. Nós encontramos que a produção de entropia escala com diferentes leis de potência nos regimes balístico e difusivo, permitindo então quantificar o \'\'custo entrópico da difusividade\'\'. Nós também computamos a CMI para cadeias de diversos tamanhos e assim encontramos leis de escala relacionando a informação compartilhada com a difusividade. Finalmente nós discutimos como esta nova perspectiva na caracterização de sistemas fora do equilíbrio pode ser aplicada para entender o problema de equilibração local em estados fora do equilíbrio. / When a quantum system is coupled to several heat baths at different temperatures, it eventually reaches a non-equilibrium steady state (NESS) featuring stationary internal heat currents. From one side, these currents are responsible to cause decorehence and produce entropy in the system. However, their existence also induce correlations between different parts of the system. In this work, we explore this two-folded aspect of NESSs. Using phase-space techniques we calculate the Wigner entropy production on general linear networks of harmonic nodes. Working in the ubiquitous limit of weak internal coupling and weak dissipation, we obtain simple closed-form expressions for the entropic contribution of each individual quasi-probability current. Our analysis also shows that, it is exclusively the (reversible) internal dynamics which maintain the stationary (irreversible) entropy production. From the informational point of view, we address how to quantify the amount of information that disconnected parts of a quantum chain share in a non-equilibrium steady-state. As we show, this is more precisely captured by the conditional mutual information (CMI), a more general quantifier of tripartite correlations than the usual mutual information. As an application, we apply our framework to the paradigmatic problem of energy transfer through a chain of oscillators subject to self-consistent internal baths that can be used to tune the transport from ballistic to diffusive. We find that the entropy production scales with different power law behaviors in the ballistic and diffusive regimes, hence allowing us to quantify what is the \'\'entropic cost of diffusivity\'\'. We also compute the CMI for arbitrary sizes and thus find the scaling rules connecting information sharing and diffusivity. Finally, we discuss how this new perspective in the characterization of non-equilibrium systems may be applied to understand the issue of local equilibration in non-equilibrium states.

Nous nous intéressons aux méthodes de contrôle de vibrations de modèles réduits de structures à n degrés de liberté, sismiquement isolées au niveau de la base par des systèmes d'isolation mixte.Le mouvement provoqué par une sollicitation sismique horizontale a lieu dans le plan vertical.Nous avons construit un problème de contrôle semi-actif de systèmes incertains soumis à des perturbations inconnues, mais bornées. Dans le langage de l'automatique, il s'agit d'un problème d'atténuation de perturbations.Le résultat principal de cette thèse porte sur la construction d'une version modifiée des résultats de Leitmann et de ses collaborateurs sur la stabilisation de systèmes non linéaires incertains. Le théorème proposé repose sur une loi de commande par retour d'état qui assure en boucle fermée les propriétés de "uniform boundedness" et "uniform ultimate boundedness".En particulier, il peut être appliqué à la résolution de problèmes de contrôle semi-actif, qui sont actuellement traités en génie parasismique.L'objectif du contrôle est d'améliorer le comportement (i.e. la réponse) de structures isolées pour faire face aux perturbations externes, c'est-à-dire les séismes. Plusieurs points différencient notre problème de la majorité que l'on trouve dans la littérature: (i) on ne s'intéresse pas seulement à la protection de la structure isolée, mais aussi aux équipements situés à l'intérieur de la structure, et (ii) au lieu d'utiliser des indicateurs de performance habituels exprimés en termes de déplacement relatif de la base versus des accélérations absolues des planchers, nous utilisons uniquement le spectre de plancher en pseudo-accélération, comme il a été proposé dans des travaux précédents par Politopoulos et Pham. Ce travail est une tentative d'utiliser explicitement les spectres de plancher comme critère de performance.Concernant la procédure d'application, plusieurs étapes intermédiaires ont été détaillées:(i) modélisation de signaux sismiques;(ii) réglage des paramètres de la loi de commande utilisant la théorie des vibrations;(iii) validation et test du comportement en boucle fermée à travers des simulations numériques: pour des raisons de simplicité, on se limite au cas n=2.Cette procédure peut être utilisée sur des structures en industrie nucléaire, mais aussi en génie civil.D'autres sujets traités incluent une tentative d'utiliser les outils temps-fréquence, et en particulier la distribution de Wigner-Ville, pour la synthèse de lois de commande, en espérant pouvoir mieux contrôler les composants transitoires des signaux de perturbation (les entrées) et des variables d'état (les sorties). / Vibration attenuation control designs are proposed for reduced plant models consisting of n-degree-of-freedom base seismically-isolated structures (i.e., a specific type of earthquake-resistant design), modeled by uncertain nonlinear systems and subjected to one-dimensional horizontal ground acceleration (i.e. the earthquake signal), treated as unknown disturbance but assumed to be bounded.In control systems literature, this is a perturbation attenuation problem.The main result of this PhD is the development of a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. The proposed theorem consists of a bounded nonlinear feedback control law that is capable of ensuring uniform boundedness and uniform ultimate boundedness in closed-loop. In particular, it can be applied to solving semi-active control design problems, which are currently dealt with in earthquake engineering.The control objective is to improve the behavior (i.e. response) of mixed base-isolated structures to external disturbance, namely earthquakes. What differentiates our problem from the majority to be found in the literature is that: (i) attention is being paid to the protection of equipment placed inside the structure an not only to the structure itself; (ii) instead of using regular performance indicators expressed in terms of relative base displacement versus floors accelerations, we use solely the pseudo-acceleration floor response spectra, as it was proposed in previous recent works by Politopoulos and Pham.Actually, this work is an attempt to explicitly use floor response spectra as performance criterion.Concerning the application procedure, some of the topics that were detailed are:(i) modeling of earthquake signals;(ii) tuning of control law parameters based on vibration theory;(iii) validation and testing of the closed-loop behavior using numerical simulations: for simplicity reasons, we take n=2.This procedure can be used on structures of both nuclear industry as well as civil engineering.Other topics include an attempt to using time-frequency concepts and in particular the Wigner-Ville distribution to the control law design procedure, in order to better control transitory components of both perturbation (the input) and state variables signals (the output).

Neste trabalho abordamos os processos de perdas colisionais por mudança de estrutura fina e por escape radiativo. Estes processos são importantes por serem os principais fatores limitantes da densidade e da permanência de átomos confinados em armadilhas magneto-ópticas. A utilização do formalismo de Wigner nos possibilitou tratar a dinâmica dos graus de liberdade internos do sistema de forma puramente quântica, enquanto tratamos os graus de liberdade translacionais de maneira semiclássica. Com este formalismo deduzimos equações inéditas para uma colisão unidimensional e desenvolvemos um algoritmo, também inédito, para a resolução numérica de tais equações. / In this work we study the collision loss processes caused by fine-structure change and radiative escape. These processes are important because they limit the density and the confinement time of atoms in magneto-optical traps. The use of the Wigner-function formalism allows us to treat the internal degrees of freedom purely quantum mechanically, while treating the dynamics of the external degrees of freedom quasi-classically. This dissertation employs this formalism to derive for the first time, quasi-classical equations describing one-dimensional cold collisions, including dissipation due to spontaneous emission, and an algorithm, also for the first time, to solve numerically the mentioned set of coupled equations.

Les entraînements électriques à base de machine asynchrone sont largement utilisés dans les applications industrielles en raison de leur faible coût, de leurs performances et de leur robustesse. Cependant, des modes de fonctionnement dégradés peuvent apparaître durant la vie de la machine. L'une des raisons principales de ces défaillances reste les défauts de roulements à billes. Afin d'améliorer la sûreté de fonctionnement des entraînements, des schémas de surveillance peuvent être mis en place afin d'assurer une maintenance préventive. Ce travail de thèse traite de la détection et du diagnostic des défauts mécaniques et plus particulièrement des défauts de roulements dans une machine asynchrone. Généralement, une surveillance vibratoire peut être mise en place. Cette méthode de surveillance est cependant souvent chère du fait de la chaîne de mesure. Une approche, basée sur l'analyse et le traitement des courants statoriques, est alors proposée, afin de suppléer à l'analyse vibratoire. L'étude est basée sur l'existence et la caractérisation des effets des oscillations du couple de charge sur les courants d'alimentation. Un schéma de détection est alors introduit pour détecter différents types de défauts de roulements. De plus, des variables mécaniques, telles que la vitesse ou le couple, sont également reconstruites afin de fournir une indication sur la présence de défauts de roulements. Par ailleurs, un diagnostic des modulations des courants statoriques est proposé, en régime permanent et en régime transitoire, quel que soit le rapport entre les fréquences porteuse et modulante. Les méthodes étudiées sont la transformée de Hilbert, la transformée de Concordia, l'amplitude et la fréquence instantanées ainsi que la distribution de Wigner-Ville. / Asynchronous drives are widely used in many industrial applications because of their low cost, high performance and robustness. However, faulty operations may appear during the lifetime of the system. The most frequently encountered faults in asynchronous drives come from rolling bearings. To improve the availability and reliability of the drives, a condition monitoring may be implemented to favor the predictive maintenance. This Ph.D. thesis deals with detection and diagnosis of mechanical faults, particularly rolling bearings defects in induction motors. Traditionally, bearing monitoring is supervised using vibration analysis. Measuring such quantities is often expensive due to the measurement system. An other approach, based on stator current analysis, is then proposed. The characterization of load torque oscillation effects on stator currents is studied. A detection scheme is then proposed to detect several types of bearing faults. Moreover, mechanical variables, such as rotating speed or torque, are estimated in order to detect bearings defects. In addition, a diagnosis of stator currents modulations is proposed, in steady and transient state, whatever the career and modulation frequencies. Hilbert transform, Concordia transform, instantaneous amplitude and frequency are studied. The Wigner-Ville distribution is used in transient state.

La caractérisation non destructive de l’adhérence des structures du type couche sur substrat est un enjeu industriel et académique important. Ce type d’échantillon est en effet utilisé pour de nombreuses applications et sa durée de vie dépend en grande partie de la qualité d’adhérence des films au substrat. Celle-ci modifie sensiblement le comportement dispersif des ondes acoustiques de surface se propageant dans de ce type de structure. Pour générer et détecter ces ondes, un dispositif Ultrasons-Laser a été privilégié. Dans un premier temps, nous avons cherché à contourner les difficultés d’interprétation rencontrées habituellement dans le contrôle de l’adhérence par ondes acoustiques de surface. Les variations d’épaisseur de la couche peuvent en effet avoir une influence sur la dispersion des ondes comparable à celle due à l’adhérence. Pour ce faire, des films polymères dont l’épaisseur est quasi-constante sont employés et apposés sur un substrat en aluminium. Ces films possèdent en plus la propriété d’être transparents. Cela permet de focaliser l’impulsion laser générant les ondes acoustiques à travers le film, directement à la surface du substrat et de placer ainsi la source acoustique à l’interface film-substrat. L’influence de la position de la source sur le comportement dispersif des ondes acoustiques de surface et par conséquent sur le contrôle de la qualité d’adhérence est alors étudiée expérimentalement ainsi qu’au travers de simulations par éléments finis. Finalement, une caractérisation de l’adhérence de différents échantillons est effectuée grâce aux courbes de dispersion obtenues à l’aide de la méthode Matrix-Pencil appliquée aux résultats expérimentaux. En utilisant un algorithme d’inversion, les raideurs d’interface caractéristiques de l’adhérence des échantillons analysés sont estimées. / The non-destructive characterization of the adhesion of layer-on-substrate structures is an important issue in industrial and academic domains. This type of sample is indeed used for many applications and its lifetime depends mainly on the adhesion of the film to the substrate. This one changes significantly the dispersive behavior of the surface acoustic waves. To generate and detect these waves, a Laser-Ultrasonics setup has been used. First, we are looking to bypass the interpretation difficulties usually encountered in the control of adhesion by surface acoustic waves. Indeed, the layer thickness variations influence the dispersion of the waves in a similar way to the adhesion. Consequently, the polymer films used have a quasi-constant thickness and they are deposited directly on an aluminum substrate. In addition, these films are also transparent. It allows us to generate directly the acoustic waves on the substrate surface, at the interface between the film and the substrate, by focusing the laser pulse through the film. In this way, the influence of the source location on the dispersive behavior of the surface acoustic waves and thus on the adhesion quality control may be studied experimentally and by using finite element simulations. Finally, a characterization of the adhesion of several samples is performed using the dispersion curves obtained applying the Matrix-Pencil method to the experimental results. An inversion algorithm allows us to estimate the interfacial stiffnesses corresponding to the adhesion of the samples.

No description available.

Neste trabalho abordamos os processos de perdas colisionais por mudança de estrutura fina e por escape radiativo. Estes processos são importantes por serem os principais fatores limitantes da densidade e da permanência de átomos confinados em armadilhas magneto-ópticas. A utilização do formalismo de Wigner nos possibilitou tratar a dinâmica dos graus de liberdade internos do sistema de forma puramente quântica, enquanto tratamos os graus de liberdade translacionais de maneira semiclássica. Com este formalismo deduzimos equações inéditas para uma colisão unidimensional e desenvolvemos um algoritmo, também inédito, para a resolução numérica de tais equações. / In this work we study the collision loss processes caused by fine-structure change and radiative escape. These processes are important because they limit the density and the confinement time of atoms in magneto-optical traps. The use of the Wigner-function formalism allows us to treat the internal degrees of freedom purely quantum mechanically, while treating the dynamics of the external degrees of freedom quasi-classically. This dissertation employs this formalism to derive for the first time, quasi-classical equations describing one-dimensional cold collisions, including dissipation due to spontaneous emission, and an algorithm, also for the first time, to solve numerically the mentioned set of coupled equations.