[pt] Interferometria tem sido utilizada para estudar uma variedade de efeitos físicos, desde os experimentos iniciais de Michelson e Morley que forneceram evidências para a teoria da relatividade restrita até os aparelhos de detecção de ondas gravitacionais utilizado no Laser Interferometer Gravitational-Wave Observatory (LIGO). O Propósito dessa dissertação é entender como explorar anyons e suas características únicas para construir interferômetros. Anyons são quasipartículas bi-dimensionais conhecidas por apresentarem estatística fracionária e possuírem aplicações em modelos de computação quântica. Para estudar sua utilidade no contexto de interferometria nós apresentamos uma perspectiva de computação quântica para experimentos de interferência. Em seguida, introduzimos modelos anyônicos e suas aplicações em computação quântica universal. Propomos um circuito quântico que implementa um certo tipo de interferômetro, e como realizá-lo em diferentes modelos anyônicos. Finalmente, discutimos um modelo de computação quântica baseado em ótica linear de anyons fermiônicos que permitiria a criação de uma versão lógica do nosso interferômetro em termos de um interferômetro físico. / [en] Interferometry has been used to study a variety of physical effects, from the early experiments of Michelson and Morley that provided evidence to special relativity to the more recent gravity-wave detection devices used by the Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment. The purpose of this thesis is to understand how one can exploit anyons and its unique characteristics to build interferometers, and understand whether there are immediate advantages in doing so. Anyons are two-dimensional quasiparticles known for their unusual fractional statistics and applications in quantum computing models. To study their usefulness in the context of interferometry, we present a quantum computational approach to interference experiments. Next we give an introduction to anyon models and how they can be used to perform universal quantum computing. We propose a quantum circuit which implements a certain type of interferometer, and how it can be realized in different anyon models. Finally, we discuss a quantum computing model based on linear optics with fermionic anyons that would enable the creation of a logical version of our interferometer in terms of a physical interferometer.

This study is inspired by a desire to revisit Anyon's Social Class and the Hidden Curriculum of Work (1980) in a more contemporary context, one that responds to calls in the research on the socioeconomic achievement gap for deeper investigation into the heterogeneity of the middle class. More specifically, the research examines five middle class American high schools in Massachusetts, and asks the question, 'How is classroom 'work' different across these schools, thirty years after Anyon's study'? This study employs several methods of analysis including Anyon's ethnographic observational analysis and a corpus linguistic analysis. It also uses reflexive interviews to review initial findings and integrate participant input into the data itself. I also draw upon the data in light of previous frameworks to develop a new framework for looking at smaller differences in teacher talk, lessons and classroom instruction that is more fit for purpose. Through these ethnographic observations and reflexive interviews, this study reveals that even across schools that are considered to belong to the same socioeconomic class - the middle class - differences in instruction and lessons can be clearly observed. The body of literature discussing the middle class, in terms of the diversity within it, is very small, this extensive study contributes to this knowledge, and hopefully creates avenues for further research. Using Anyon's approach of observing 'work' across social class in classrooms this research builds on Anyon's findings in a contemporary context. Insight into the ways in which difference manifests in smaller ways in the classroom may be fundamental in understanding how small differences compound across the socioeconomic spectrum. The impact of this research on the socioeconomic achievement gap is a better, more complete, look at the picture of how the distribution of resources across the socioeconomic spectrum plays a role in classroom differences.

No description available.

Les isolants topologiques sont des isolants qui ne peuvent être différenciés des isolants atomiques que par une grandeur physique non locale appelée invariant topologique. L'effet Hall quantique et son équivalent sans champ magnétique l'isolant de Chern sont des exemples d'isolants topologiques. En présence d'interactions fortes, des excitations exotiques appelées anyons peuvent apparaître dans les isolants topologiques. L'effet Hall quantique fractionnaire (EHQF) est la seule réalisation expérimentale connue de ces phases. Dans ce manuscrit, nous étudions numériquement les conditions d'émergence de différents isolants topologiques fractionnaires. Nous nous concentrons d'abord sur l'étude de l'EHQF sur le tore. Nous introduisons une méthode de construction projective des états EHQF les plus exotiques complémentaire par rapport aux méthodes existantes. Nous étudions les excitations de basse énergie sur le tore de deux états EHQF, les états de Laughlin et de Moore-Read. Nous proposons des fonctions d'onde pour les décrire, et vérifions leur validité numériquement. Grâce à cette description, nous caractérisons les excitations de basse énergie de l'état de Laughlin dans les isolants de Chern. Nous démontrons également la stabilité d'autres états de l'EHQF dans les isolants de Chern, tels que les états de fermions composites, Halperin et NASS. Nous explorons ensuite des phases fractionnaires sans équivallent dans la physique de l'EHQF, d'abord en choisissant un modèle dont l'invariant topologique a une valeur plus élevée, puis en imposant au système la conservation de la symétrie par renversement du temps, ce qui modifie la nature de l'invariant topologique. / Topological insulators are band insulators which are fundamentally different from atomic insulators. Only a non-local quantity called topological invariant can distinguish these two phases. The quantum Hall effect is the first example of a topological insulator, but the same phase can arise in the absence of a magnetic field, and is called a Chern insulator. In the presence of strong interactions, topological insulators may host exotic excitations called anyons. The fractional quantum Hall effect is the only experimentally realized example of such phase. In this manuscript, we study the conditions of emergence of different types of fractional topological insulators, using numerical simulations. We first look at the fractional quantum Hall effect on the torus. We introduce a new projective construction of exotic quantum Hall states that complements the existing construction. We study the low energy excitations on the torus of two of the most emblematic quantum Hall states, the Laughlin and Moore-Read states. We propose and validate model wave functions to describe them. We apply this knowledge to characterize the excitations of the Laughlin state in Chern insulators. We show the stability of other fractional quantum Hall states in Chern insulators, the composite fermion, Halperin and NASS states. We explore the physics of fractional phases with no equivalent in a quantum Hall system, using two different strategies: first by choosing a model with a higher value of the topological invariant, second by adding time-reversal symmetry, which changes the nature of the topological invariant.

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac statistics.