Les oscillations dans le plasma d'un propulseur à effet Hall sont susceptibles de provoquer le transport anormal à travers des lignes du champ magnétique. La théorie cinétique linéaire montre qu'en particulier certaines oscillations, de fréquence de l'ordre du mégahertz et de longueur d'onde millimétrique, peuvent jouer un rôle important dans le transport anormal. Les échelles caractéristiques de ces fluctuations ne sont pas détectables par des outils standards comme les sondes. Ce travail décrit pour la première fois l'utilisation d'un diagnostic de diffusion collective (PRAXIS) conçu pour l'étude du plasma du propulseur, qui a mené à l'identification des modes instables dans le plasma. Deux modes hautes fréquences ont été identifiés, se propageant dans les directions azimutale et axiale, avec des longueurs d'onde millimétriques et des fréquences de l'ordre du mégahertz. Les directions de propagation et les ouvertures angulaires de ces modes ont été déterminées. Le mode azimutal, identifié dans la théorie comme agent principal du transport, possède des composantes anti-parallèles au champ magnétique et parallèles au champ électrique et se propage dans une ouverture angulaire très restreinte. Le mode axial montre des caractéristiques liées à la vitesse et la divergence du faisceau d'ions. Le niveau de fluctuation de la densité est associé à une grande amplitude du champ électrique fluctuant. Les résultats des expériences sont en accord avec les prévisions théoriques et apportent de nouvelles informations, permettant ainsi d'améliorer et de développer des modèles pour les deux modes.

We consider the purity-based entanglement detection scheme introduced in [C. Moura Alves and D. Jaksch, Phys. Rev. Lett. 93, 110501 (2004)]. We describe how it could be implemented in an optical lattice using two-atom loss, and prove that in this form it detects all pure entangled states even without any spatial resolution. We then prove that correcting for certain reasonable types of experimental error is possible, and practical for error rates up to the order of one over the number of lattice sites considered. Limited spatial resolution similarly becomes a significant improvement over no spatial resolution only at nearly single site level. We also show how to use this process for state parameter estimation and collapse-revival evidence of entanglement, for which it remains useful even when the error rate is too high to permit unambiguous entanglement detection. We also consider an optical lattice bosonic analogue of the fractional quantum Hall (FQH) effect. This system can reach high “magnetic fields” very difficult to attain in the solid state FQH system, where the discrete nature of the lattice becomes important. Near simple rational numbers l/n of flux quanta per lattice cell, we find that the single particle states become nearly periodic with period n lattice sites, and have an n fold degeneracy which leads to FQH states resembling those of n-internal-state particles. Standard time of flight expansion would reveal this periodicity and be able to distinguish FQH states from vortex lattice or Mott insulator states. Shot noise correlation would provide further information on the nature of the FQH states.

This thesis describes the design and construction of a novel two-phase spherical electric machine that generates rotating uniform magnetic fields, known as a fluxball machine. Alternative methods for producing uniform magnetic fields with air-cored solenoidal magnets are discussed and evaluated. Analytical and numerical models of these alternatives are described and compared. The design details of material selection, slot geometry, and mechanical connections are described for the fluxball machine. The electrical properties of the machine are predicted and measured. Based on these properties, two modes of operation for the fluxball machine, normal and resonant, are described, and reference tables of important operating parameters are given. The drive and measurement circuitry for the fluxball machine are described. The magnetic properties of the fluxball machine are measured using Hall effect sensors. The calibration of two different Hall effect sensors is performed, providing the ability to measure the magnetic fields accurately to +or- 1%. Measurements of the magnetic field in the uniform field region are taken and compared with predicted values. The attenuation and distortion of the magnetic fields due to diffusion through the inner fluxball winding is measured as a function of operating frequency. Finally, future uses of this machine for various applications are discussed. / Contract number: N62271-97-G-0026 / US Navy (USN) author.

Les producteurs d’aluminium sont des acteurs majeurs dans l’économie du Québec. Le métal gris est apprécié pour sa légèreté et sa résistance à la corrosion. Bien qu’il possède des qualités indéniables, sa production consomme une quantité considérable d’électricité. L’amélioration de l’efficacité énergétique du procédé est donc primordiale d’un point de vue économique et environnemental. L’étude du contact électrique entre le carbone et la fonte à l’intérieur de l’ensemble cathodique fait partie de la liste des paramètres pour optimiser la consommation énergétique de la cellule Hall-Héroult. Ce contact doit offrir une résistance minimale au passage du courant nécessaire pour la réaction d’électrolyse. Au cours du temps, la qualité du contact se dégrade en raison de la transformation physique et chimique des matériaux. Cette thèse se concentre sur l’étude de la dégradation chimique de la surface de la fonte. La première partie étudie la pénétration des composés chimiques provenant du bain d’électrolyse à l’intérieur du bloc de carbone. Le gonflement sodique suit généralement la diffusion du sodium, un sous-produit de la réaction cathodique, et du bain. Le gonflement causé par le sodium a été mesuré directement à l’aide de LVDT alors que la diffusion du bain électrolytique a été déterminée par microtomographie à rayons X. La seconde partie évalue le mécanisme de la dégradation du contact électrique entre le carbone et la fonte. Des travaux en laboratoire ont été réalisés pour quantifier l’impact des paramètres d’opération. Les résultats obtenus ont été comparés par la suite à des échantillons industriels provenant de deux technologies pour évaluer leur degré de dégradation. Un modèle numérique a été calibré à partir de ces résultats pour estimer l’effet de la dégradation de la fonte sur la chute de voltage cathodique. Les résultats démontrent que les paramètres d’opération de la cellule d’électrolyse ont des effets sur la vitesse de pénétration des espèces chimiques dans le bloc de carbone. Un bain plus riche en sodium ou une densité de courant cathodique plus élevée augmente la vitesse de pénétration. La présence d’une nappe d’aluminium au démarrage de l’électrolyse au contraire divise le gonflement et la pénétration du bain de moitié. La vitesse de dégradation de la fonte suit la même tendance. De plus, une augmentation de température de 50 °C provoque une fusion partielle de la surface de la fonte. Ces résultats intégrés au modèle numérique montre que la dégradation du contact entre le carbone et la fonte augmente la chute de voltage cathodique mais aussi change la distribution du courant à la surface du bloc de carbone. La détermination du mécanisme de dégradation de la fonte par des essais en laboratoire combinée avec la pénétration des espèces chimiques constitue l’apport original de cette thèse et ceci permet d’éclaircir le processus d’évolution de ce contact électrique sous condition d’opération.

This thesis scrutinizes the condensed matter physics phenomenon known as the fractional quantum Hall effect (FQHE), in particular fractional quantum Hall effects occurring in multicomponent systems. Broadly speaking, the FQHE can be defined as a many-electron quantum phenomenon, driven by strong interactions, that occurs in two-dimensional electron gasses in the presence of a perpendicular external magnetic field (and it is also predicted to occur for any two-dimensional particles, such as confined cold atoms, in an external gauge field). Multicomponent systems are systems where the constituent particles (such as electrons or cold atoms) possess internal degrees of freedom, for instance a spin or valley index. These internal degrees of freedom are often overlooked when modeling the FQHE. Taking into account the multicomponent degree of freedom yields an abundance of possibilities for the intellection of new types of so-called “topological phases of matter”, which are ubiquitously associated with the FQHE. In this thesis several different cases are considered. The first topic discussed herein is a study of phase transitions that can take place between FQHE phases with different net values of their multicomponent degrees of freedom. Examples are phase transitions between phases of different uniform net spin polarization, tunable as a function of certain system parameters. Some significant technical refinements are made to a previous model and comparisons are made with a variety of different experiments. The results are relevant for multicomponent FQHEs occurring in GaAs,AlAs and SiGe semiconductor systems where the electronic structure is confined to two dimensions, as well as in two-dimensional materials such as graphene. The second topic discussed herein is the introduction of the multiparticle multicomponent pseudopotential formalism. This methodology is oriented towards considerably expanding an existing framework for the construction of exactly solvable FQHE models by parameterizing multicomponent interactions. The final topic is the first example application of this new formalism to the construction of an exactly solvable FQHE model.

This research is related to British banking-halls as a class of real estate investment. Sale-and-leaseback has become an increasingly common approach during the last two decades for the holding of British banking-halls. One measure used in making property investment decisions is the all risks yield (ARY). Investors and their advisors have a need for a predictive framework which they can use for predicting those retail bank premises likely to achieve the highest ARY when assembling investment portfolios of such properties. A predictive framework necessitates the identification of those factors significantly influencing the yields of British banking-halls. This research aims to develop such a framework. Triangulation methodology was adopted to establish and test the predictive framework. A literature review established theory before a qualitative study, based upon semi-structured interviews and a questionnaire, was used to establish the influencing factors. A cross-sectional study of auction data then formed the basis of the quantitative regression study. The qualitative and quantitative studies validated that four factors were significant in influencing yield. These were tenant banking company, lot size, super-region and the macro-economic cycle index. A toolkit comprising a predictive framework for those banking-halls likely to produce the highest ARY was produced. This is capable of being used by professional practitioners and investors in predicting high yield for portfolio building purposes. The predictive framework was developed based upon the quantitative data from those three banks with the most premises sold by sale-and-leaseback. It formed a baseline from which further studies can build to test its significance for other banks. Consequently, a more robust predictive framework can be developed for banking-hall investments. Further research can also be conducted to develop predictive frameworks forecasting yields for investment in other commercial retail sectors, based upon the findings of this research.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Les progrès technologiques dans la fabrication des semi-conducteurs permettent, depuis le début des années 80, de réaliser des dispositifs dans lesquels les électrons sont fortement confinés dans un plan, on parle de système d'électrons bidimensionnels. L'application d'un champ magnétique perpendiculaire intense à ce système permit l'observation des effets Hall quantiques (EHQ), entier en 1980 puis fractionnaire en 1982. En présence du champ magnétique et aux températures extrêmement faibles qui sont concernées, le spectre énergétique des électrons bidimensionnels est quantifié en niveaux de Landau macroscopiquement dégénérés. Le comportement du système est alors déterminé par le facteur de remplissage des niveaux de Landau. L'EHQ entier apparaît autour des valeurs de champ magnétiques qui correspondent à un remplissage entier des niveaux Landau, tandis que son pendant fractionnaire est obtenu autour de certaines fractions du facteur de remplissage ν (ν =1/3, 2/5, 5/2, …) . Alors qu'à remplissage ν entier c'est le comportement individuel des électrons qui gouverne le comportement du système, aux facteurs de remplissage fractionnaires les corrélations électroniques dominent. En raison de ce caractère fortement corrélé, l'EHQ fractionnaire sous-tend un effort de recherche expérimental et théorique important depuis sa découverte. En effet, dans le régime fractionnaire les corrélations fortes induisent des propriétés inédites telles l'existence de quasi-particules de charge fractionnaire, mais elles rendent également la description théorique du système ardue. En 1983, Robert Laughlin proposa une fonction d'onde variationnelle modèle pour la description de l'EHQ fractionnaire observé à remplissage ν=1/3, dont il discuta la validité au regard d'une étude numérique approfondie des interactions entre les électrons. Le succès de cette méthode l'éleva au rang de paradigme, et de nombreuses fonctions d'onde d'essai ont depuis été proposées pour l'explication des effets Hall quantiques observés aux autres facteurs de remplissages. Notamment, la fonction d'onde de Moore et Read s'avère pertinente pour la description de l'EHQ observé à demi-remplissage du second niveau de Landau. Celle-ci suggère l'existence de quasi-particules non-abéliennes qui génère des espoirs importants de par ses applications potentielles en informatique quantique protégée topologiquement. Bien que l'EHQ ait également été observé à demi-remplissage du plus bas niveau de Landau, la nature de l'état sous-jacent est encore débatue. Celui-ci n'est observé que dans les systèmes bicouches et dans les puits larges qui sont au centre de ce travail de thèse. Les puits larges désignent les systèmes dans lesquels l'épaisseur du système d'électrons bidimensionnel ne peut plus être négligée, typiquement à des épaisseurs de l'ordre de 100 nm. En raison du potentiel de confinement ressenti par les électrons, leurs niveaux d'énergies dans la direction du confinement sont quantifiés en sous-bandes. Dans un puits extrêmement fin seule la plus basse sous-bande est peuplée et le degré de liberté correspondant est alors gelé, mais dans les puits large les sous-bandes excitées sont pertinentes. Dans ces conditions l'EHQ fractionnaire à demi-remplissage peut également résulter de la stabilisation d'un état à deux composantes qui peuple les sous-bande excitées. Cet état proposé par Bertrand Halperin en 1983 entre en compétition avec l'état de Moore et Read. En plus de ces deux états, un état métallique de fermions composite est possible, ainsi qu'un cristal électronique de Wigner au comportement isolant. La compétition entre ces différents états est arbitrée par une étude de Monte-Carlo variationnel combinée à des calculs de diagonalisation exacte. La nature de l'état qui est stabilisé dépend de la nature du potentiel de confinement. Dans ce manuscrit de thèse sont discutés les dispositifs de la bicouche, du puits large, ainsi que du puits large en présence d'un biais externe. / Due to technological advances in the manufacture of semiconductors enable, in it possible since the early 80s to create devices in which electrons are strongly confined in a plane, thus effectively realizing a two-dimensional electron system. The application of a strong perpendicular magnetic field to this system led to the observation of the integer quantum Hall effect (QHE) in 1980 and fractional QHE in 1982. Under a strong magnetic field the energy spectrum of the two-dimensional electrons is quantified in Landau levels that are macroscopically degenerate, and the behavior of the system is governed by the filling factor of Landau levels. The integer QHE appears around magnetic field values ​​which correspond to an integer filling of the Landau levels, while the fractional equivalent is obtained around certain fractions of the filling factor ν (ν = 1/3, 2/5, 5 / 2, ...). Although for integers values of ν is the individual behavior of electrons dictates the behavior of the system, the fractional filling factors the electronic correlations dominate. Because of those strong correlations, the underlying fractional QHE motivates an important experimental and theoretical research effort since its discovery. Indeed, in the fractional regime the strong correlations induce novel properties such as the existence fractionally-charged quasiparticles, but they also make the theoretical description of the system laborious. In 1983 Robert Laughlin proposed a variational wave function model for the description of the QHE observed at fractional filling ν = 1/3. He discussed the validity of this trial wave function in a comprehensive numerical study of interactions between electrons. The success of this method made it a paradigm, and many test wave functions have been proposed since then for the explanation of quantum Hall effects observed with other fillings factors. In particular, the wave function of Moore and Read is relevant for the description of the QHE observed at half-filling the second Landau level. This suggests the existence of non-Abelian quasiparticles with potential applications in topologically-protected quantum computing. QHE has also been observed at half filling the lowest Landau level, but the nature of the underlying quantum state is still debated; it is observed that in bilayer systems and wells wide. The large wells, which are the focus of this thesis, refer to systems in which the thickness of the two-dimensional electron system cannot be trivially neglected and usually corresponds to a thickness of about 100 nm. Due to the confinement potential felt by the electrons, their energy levels in the direction of confinement are quantized in sub-bands. In a narrow well only the lowest subband is populated and the corresponding degree of freedom is thus frozen, but in a wide well the excited sub-bands are relevant. Under these conditions fractional QHE at half-filling can also result from the stabilization of a two-state components that also populates the excited sub-band. The corresponding trial state, proposed by Bertrand Halperin in 1983, competes with the state of Moore and Read. In addition to these two states, a metal composite fermion state is a relevant trial state as well as an electronic Wigner crystal, the latter behaving as an insulator. The competition between these states is refered by a variational Monte-Carlo study combined with exact diagonalization calculations. The nature of the state that is stabilized depends on the nature of the confinement potential. In this PhD thesis three confinement potentials are studied: the bilayer, the wide well, and the wide well in the presence of an external bias.

Este trabalho apresenta as propriedades de transporte eletrônico de isolantes topológicos bidimensionais (TI) baseados em poços quânticos de HgTe/CdTe. Estas heteroestruturas, no regime de bandas invertido, contem um novo estado conhecido como isolante de spin Hall quântico (QSHI). Este estado apresenta um comportamento de isolante no corpo (bulk), mas exibe estados condutores sem lacunas nas bordas (edges), as quais podem ser verificadas em medidas de transporte. Medidas de resistência de quatro terminais foram observadas perto do valor quantizado em amostras mesoscópicas. No entanto, para amostras com mais de um m, a resistência pode ser muito maiores que h/2e2 devido à presença de defasagem de spin, não homogeneidade ou desordem na amostra. Esta tese aborda o problema da resistência não quantizado observada em amostras macroscópicas de dimensões maiores a algum mícron. Nós relatamos observação e investigação sistemática de transporte local e não local em poços quânticos de HgTe (8.0-8.3 nm) com estrutura de banda invertida correspondente à fase de isolante de spin Hall quântico. O dispositivo MCT1 consiste de três segmentos consecutivos de largura 4 m e de comprimentos diferentes (2 m, 8 m, 32 m), e sete sondas de tensão. O dispositivo MCT2 foi fabricado com um comprimento litográfico de 6 m e largura 5 m. Ambos dispositivos estão equipados com uma porta superior (top gate), que permite ajustar a densidade de portadores do dispositivo. A aplicação de uma tensão de porta muda a densidade de portadores, transformando a condutividade do poço quântico de tipo n para tipo p através de uma fase intermediária chamada de ponto a neutralidade de carga (CNP). Picos acentuados não universais (R >> h/2e2) em ambas as resistividades, local e não local, foram observados próximos ao CNP os quais diminuem rapidamente a medida que se afasta do CNP. Tal comportamento próximo ao CNP pode ser explicado usando o modelo de transporte de bordas (edge) e corpo (bulk), que inclui tanto os estados de borda como o corpo para a contribuição à corrente. O desvio dos valores da resistência de quarto terminais do valor quantizado (R >> h/2e2) em amostras macroscópicas com dimensões acima de algum mícron é um dos principais problemas no campo dos isolantes topológicos. Recentemente foi proposto um modelo por Vayrynen et al., onde tem sido considerado a influência de poças de carga, resultantes de distribuições de carga não homogêneas em isolantes topológicos 2d, na condutância de estados de borda helicoidal. Os estados de borda são acoplados por tunelamento a essas poças metálicas ou pontos quânticos. A permanência dos elétrons em pontos quânticos pode levar a um retroespalhamento inelástico significativo dentro da borda e modifica o transporte balístico. Portanto transporte balístico coerente é esperado somente na região entre poças, e o total de resistência de quatro terminais excede o valor quantizado. Introduzindo as interações elétron-elétron em sistemas de uma dimensão resulta em um liquido de Luttinger (LL). Os estados de borda helicoidais em isolantes topológicos 2d, podem ser tratados como um líquido de Luttinger ideal, uma vez que, naturalmente, aparecem em poços quânticos de HgTe. Entre as várias assinaturas específicas do comportamento do LL, como a dependência da temperatura, é importante se concentrar nas propriedades de não equilíbrio do LL. Em contraste com os líquidos de Fermi convencionais, nenhum estado excitado decairá ao estado de equilíbrio, caracterizado pela temperatura, na ausência de desordem. Medidas de elétron-aquecimento podem ser usadas para entender a física que governa os processos de relaxamento em LL. Nós temos realizado medidas de transporte não linear no CNP em isolantes topológicos 2d de HgTe. Este método, juntamente com a dependência da resistência com a temperatura, pode ser utilizado para determinar o mecanismo de relaxação da energia dos estados de borda helicoidais em QSHI. Nosso experimento falhou em confirmar as assinaturas especificas do comportamento do líquido de Luttinger. No entanto, o efeito de aquecimento de elétron pode ser descrito pelo mecanismo convencional de relaxamento de energia, esperado para espalhamento elétron-fônon. / This thesis present electronic transport properties of two-dimensional topological insulators (TI) based on HgTe/CdTe quantum wells. These heterostructures, in the band inverted regime, hosts a novel state known as the quantum spin Hall insulator. This state is identified as insulator in the bulk, but exhibits gapless conducting states at their edges which can be verified in transport experiments. Four-terminal resistance close to the quantized value has been observed in mesoscopic samples. However, for samples longer than 1 m, the resistance might be much higher than h/2e2 due to the presence of spin dephasing, inhomogeneity or disorder in the sample. This thesis address the problem of non-quantized resistance observed in macroscopic samples of dimensions longer than few microns. We report on the observation and a systematic investigation of local and nonlocal transport in HgTe quantum wells (8.0-8.3 nm) with inverted band structure corresponding to the quantum spin Hall insulating (QSHI) phase. The device MCT1 consists of three 4 m wide consecutive segments of different length (2 m, 8 m, 32 m), and seven voltage probes. The device MCT2 was fabricated with a lithographic length 6 m and width 5 m. Both devices are equipped with a top gate which allows tuning the carrier density of the device. Applying gate bias changes the carrier density transforming the quantum well conductivity from n-type to p-type via an intermediate phase, called the charge neutrality point (CNP). Non-universal (R >> h/2e2) peaks in both local and nonlocal resistivity were observed near the CNP which decreases rapidly going away from CNP. Such a behavior near CNP can be explained using the edge plus bulk transport model, which includes both the edge states and bulk contribution to the total current. Deviation of the four-terminal resistance from quantization (R >> h/2e2) in macroscopic samples, with dimensions above a few microns, is one of the major issue in the field of topological insulators. Recently a model was proposed by Vayrynen et al., where influence of charge puddles, resulting from inhomogeneous charge distribution in 2d topological insulators, on its helical edge conductance has been considered. The edge states are tunnel coupled to these metallic puddles or quantum dots. Electron´s dwelling in the quantum dot may lead to significant inelastic backscattering within the edge and modifies the ballistic transport. Therefore ballistic coherent transport is expected only in the region between the puddles, and the total four-terminal resistance exceeds the quantized value. Introducing electron-electron interactions in one-dimensional systems results in a Luttinger liquid (LL). The helical edge states in 2d topological insulator, can be treated as ideal Luttinger liquid, since it naturally appears in HgTe quantum wells. Among the various specific signatures of the LL behavior, such as temperature dependence, it is important to focus on non-equilibrium properties of LL. In contrast to conventional Fermi liquids, none of the excited state will decay to equilibrium state, characterized by temperature, in the absence of disorder. Electron-heating measurements can be used to understand the physics governing relaxation processes in LL. We have performed non-linear transport measurements at the CNP in HgTe based 2d topological insulators. This method together with temperature dependence of resistance can be used to determine the energy relaxation mechanism of the helical edge modes in QSHI. Our experiments fail to confirm the specific signatures of Luttinger liquid behavior. However, electron heating effect can be described by conventional energy relaxation mechanism, expected for electron-phonon interactions.

We consider a series of problems regarding quantum Hall edges, focusing on both dynamics and the mathematical structure of edge states. We begin in Chapter 3 with a limiting case of the Laughlin state placed in a very steep confining potential, but which is weak compared to the interactions. We find that the eigenstates have a Jack polynomial structure and an energy spectrum which is extremely different from the well-known Luttinger liquid edge. In Chapter 5 we analyse the inner products of edge state wavefunctions, using an effective description given by a large-N expansion ansatz proposed by J. Dubail, N. Read and E. Rezayi, PRB 86, 245310 (2012). As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check the conjecture by calculating overlaps exactly for small system sizes and comparing the numerics with our high-order expansion to find excellent agreement. Finally, Chapter 6 considers the behaviour of quantum Hall edges close to the Luttinger liquid fixed point that occurs in the low energy, large system limit. We construct effective Hamiltonians using a local field theory description and then consider the effect of bulk symmetries on this edge. The symmetry analysis produces remarkable simplifications which allow for very accurate descriptions of the low-energy edge physics even relatively far away from the Luttinger liquid fixed point.