Thesis advisor: Solomon Friedberg / Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondly, we determine the unipotent orbits attached to theta functions, in the sense of Ginzburg. We also determine the covers for which these models are unique. We also describe briefly some applications of these unique models in Rankin-Selberg integrals for covering groups. / Thesis (PhD) — Boston College, 2017. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

A Prótese Buco Maxilo Facial é a especialidade da Odontologia responsável pela confecção de próteses intra e extra-bucais, indicadas quando regiões maxilofaciais foram perdidas. Implantes craniofaciais podem servir como ancoragem para próteses faciais, inclusive as óculo-palpebrais. O presente trabalho teve como propósito avaliar o comprimento e a espessura da estrutura óssea da região periorbitária e realizar a validação do método de mensuração proposto. Foram realizadas mensurações lineares de comprimento e largura das corticais ósseas das regiões peri-orbitárias em tomografias computadorizadas de 30 crânios humanos secos. Dois examinadores realizaram as mensurações, duas vezes cada um, com intervalos de no mínimo 7 dias, em pontos de referência determinados de acordo com as horas de um relógio. A análise estatística revelou que, para a grande maioria das medidas, as variações intra e inter-examinadores não apresentaram diferenças significantes (p<0,05), indicando que o método de mensuração proposto é confiável e válido para a mensuração da região peri-orbitária. Verificou-se que os três pontos de maior comprimento seguiram a mesma seqüência anatômica para as órbitas direita e esquerda, localizando-se no rebordo supra-orbitário e sendo compatíveis com a inserção de implantes osseointegráveis intra-bucais. Os três pontos localizados na parede lateral e na região látero-inferior da órbita apresentaram comprimento compatível com a utilização de implantes osseointegráveis intra-bucais. A parede medial de ambas as órbitas não apresentou comprimento favorável à inserção de implantes intra-bucais ou crânio-faciais. Os pontos de maior largura foram observados no rebordo supra-orbitário e na região látero-inferior de ambas as órbitas, e aqueles de menor largura foram encontrados na região látero-superior de ambas as órbitas. / The Maxillofacial Prosthesis is the dental specialty responsible for the confection of extra and intra-oral prosthesis indicated when facial regions have been lost. Craniofacial osseointegrated implants made possible the confection of implantretained facial prosthesis, namely the orbital prosthesis. This work aimed to evaluate the length and the thickness of the bone structure of the periorbital region and to present the validation of the method. Computer tomographies of 30 dry human skulls were made in order to register linear length and width measurements of the periorbital region. Two examiners, two times each one, took the measurements with intervals of at least 7 days between the measurements. Statistics pointed out that, for most instances, the intra and inter-examiners variations were not significant (p<0.05). Therefore, the method proposed is precise and valid for the measurement of the periorbital region. It was verified that the three points with deeper values followed the same anatomical sequence in the supraorbital rim for the right and left orbits, being compatible with the insertion of intraoral osseointegrated implants. The medial wall of both orbits did not present enough length to allow the insertion of intraoral or craniofacial implants. The points of larger width were observed in the supraorbital rim and in the infralateral region of both orbits, and those of smaller width were found in the supralateral region of both orbits.

Apresento neste trabalho uma derivação alternativa da hamiltoniana efetiva para um elétron na banda de condução de uma heteroestrutura semicondutora de rede Zincblende. Partindo do modelo de Kane 8 × 8 e da aproximação das funções envelope, esta hamiltoniana efetiva foi obtida com a linearização dos denominadores (dependentes das autoenergias) presentes na equação para a banda de condução, sob a hipótese de que o gap de energia seja muito maior que todas as demais diferenças de energia envolvidas (verdade para a maioria das estruturas Zincblende). A partir de um procedimento introduzido previamente1,3, desenvolvi um procedimento mais geral que implementa sistematicamente esta linearização até segunda ordem no inverso do gap de energia e que corrige a normalização do spinor da banda de condução usando as bandas de valência. Este procedimento é idêntico à expansão em série de potência no inverso da velocidade da luz utilizada para se obter aproximações relativísticas da equação de Dirac. Uma vantagem deste procedimento é a arbitrariedade na forma dos potenciais, o que implica na validade da hamiltoniana resultante para poços, fios e pontos quânticos. Evidencio também as consequências de cada termo desta hamiltoniana efetiva para os autoestados eletrônicos em poços retangulares, incluindo termos independentes de spin inéditos (Darwin e interação momento linearcampo elétrico). Estes resultados estão de acordo com os estudos anteriores4. A fim de estudar transições ópticas dentro da banda de condução, mostro que o acoplamento mínimo pode ser realizado diretamente na hamiltoniana de Kane se os campos externos variam tão lentamente quanto as funções envelope. Repetindo a linearização dos denominadores de energia, derivo uma hamiltoniana efetiva para a banda de condução com acoplamentos elétron-fótons. Um destes acoplamentos, induzido exclusivamente pela banda de valência, origina transições mediadas pelo spin eletrônico. Estas transições assistidas por spin possibilitam mudanças, opticamente induzidas, na orientação do spin eletrônico, um fato que talvez possa ser útil na construção de dispositivos spintrônicos. Por fim, as taxas de transição deste acoplamento apresentam saturação e linhas de máximos e mínimos no espaço recíproco. Espero que estas acoplamentos ópticos possam auxiliar na observação dos efeitos dos acoplamentos spin-órbita intra (Rashba) e intersubbandas. / In this work, I present an alternative derivation of the conduction band effective hamiltonian for Zincblende semiconductor heterostructures. Starting from the 8×8 Kane model and envelope function approximation, this effective hamiltonian was obtained by means of a linearization in the eigenenergy-dependent denominators present the conduction band equation, under the hypothesis that the energy gap is bigger than any other energy difference in the system (true for mostly every Zincblende semiconductor bulk or heterostructure). Based on a previous procedure1,3, I have developed a more general procedure that implements sistematicaly (i) this linearization and (ii) renormalizes the conduction band spinor using the valence bands, both (i) and (ii) up to second order in the inverse of the energy gap. This procedure is identical to the expansion in power series of the inverse of the light speed used to derive non-relativistic approximations of the Dirac equation. One advantage of this procedure is the generality of the potentials adopted in our derivation: the same results hold for quantum wells, wires and dots. I show the consequences of each term of this hamiltonian for the electron eigenstates in retangular wells, including novel spin-independent terms (Darwin and linear momentumelectric field couplings). These resulties agree with previous works4. In order to study conduction band optical transitions, I show that the minimal substitution can be performed directly in the Kane hamiltonian if the external fields vary slowly (at least, as slowly as the envelope functions). Repeating the linearization of the energy denominators, I derive a new effective hamiltonian, up to second order in the inverse of the energy gap, with electron-photons couplings. One of these couplings, induced exclusively by the valence bands, gives rise to optical transitions mediated by the electron spin. This spin-assisted coupling enable optically-induced spin flipps in conduction subband transitions, which can be useful in the construction of spintronic devices. Finaly, the spin-assisted transitions rates show saturation and lines of maxima and minima in the reciprocal lattice. I hope that these optical couplings can be of any help in the observation of interesting effects induced by the intra and intersubband spin-orbit coupling.

In the context of future human space exploration missions in the solar system (with an horizon of 2025) and according to the roadmap proposed by ISECG (International Space Exploration Coordination Group) [1], a new step could be to maintain as an outpost, at one of the libration points of the Earth-Moon system, a space station. This would ease access to far destinations as Moon, Mars and asteroids and would allow testing some innovative technologies, before employing them for far distant human missions. One of the main challenges will be to maintain permanently, and ensure on board crew health thanks to an autonomous space medical center docked to the proposed space station, as a Space haven. Then the main problem to solve is to manage the station servitude, during deployment (modules integration) and operational phase. Challenges lie, on a global point of view, in the design of the operational scenarios and, on a local point of view, in trajectories selection, so as to minimize velocity increments (energy consumption) and transportation duration (crew safety). Which recommendations could be found out as far as trajectories optimization is concerned, that would fulfill energy consumption, transportation duration and safety criterion? What would technological hurdles be to rise for the building of such Space haven? What would be performances to aim at for critical sub-systems? Expected results of this study could point out research and development perspectives for human spaceflight missions and above all, in transportation field for long lasting missions. Thus, the thesis project, presented here, aims starting from global system life-cycle decomposition, to identify by phase operational scenario and optimize resupply vehicle mission. The main steps of this project consist of: - Bibliographical survey, that covers all involved disciplines like mission analysis (Astrodynamics, Orbital mechanics, Orbitography, N-Body Problem, Rendezvous…), Applied Mathematics, Optimization, Systems Engineering…. - Entire system life-cycle analysis, so as to establish the entire set of scenarios for deployment and operations (nominal cases, degraded cases, contingencies…) and for all trajectories legs (Low Earth Orbit, Transfer, Rendezvous, re-entry…) - Trade-off analysis for Space Station architecture - Modeling of the mission legs trajectories - Trajectories optimization Three main scenarios have been selected from the results of the preliminary design of the Space Station, named THOR: the Space Station deployment, the resupply cargo missions and the crew transportation. The deep analysis of those three main steps pointed out the criticality of the rendezvous strategies in the vicinity of Lagrangian points. A special effort has been set on those approach maneuvers. The optimization of those rendezvous trajectories led to consolidate performances (in term of energy and duration) of the global transfer from the Earth to the Lagrangian point neighborhood and return. Finally, recommendations have been deduced that support the Lagrangian points importance for next steps of Human Spaceflight exploration of the Solar system.

Para oferecer mais informações aos cirurgiões no planejamento de intervenções cirúrgicas maxilofaciais, o presente estudo teve como objetivo avaliar a presença, localização e tamanho dos canais alveolares superiores (CAS), anterior (CASA) e posterior (CASP), canal infra-orbital (CI) e forame infra-orbital (FI) em imagens de tomografia computadorizada de feixe cônico (TCFC) de 100 pacientes adultos (&#x2265; 20 anos), obtidas pelo aparelho i-CAT Classic®. Um examinador calibrado observou a presença dos CAS, CI e FI bilateralmente. Quando presentes, eram medidos comprimento (parte descendente, parte do assoalho da órbita e total), largura e altura do CI; altura, largura e distância ao rebordo inferior da órbita (RIO) do FI; distância da borda inferior dos CAS a crista do rebordo alveolar em 5 regiões: canino (CAN), primeiro pré-molar (1PM), segundo pré-molar (2PM), primeiro molar (1M) e segundo molar (2M); e os diâmetros dos CAS. Foram também observados a localização dos CAS em relação ao seio maxilar e a presença de reparos anatômicos como canal duplo/múltiplo, anastomose intra-óssea e extensão do CASA para a abertura piriforme. Associações entre homens e mulheres, lados direito e esquerdo e regiões foram investigadas para todas as medidas e visibilidade, utilizando separadamente os métodos estatísticos. A presença do CI e FI foi de 100%. A visibilidade do CASA/CASP foi de: 99%/0% (CAN), 99%/21% (1PM), 89%/41% (2PM), 46%/44% (1M) e 7%/61% (2M). As médias dos comprimentos da parte descendente, da parte do assoalho da órbita e total do CI foram de 8,82mm, 19,44mm e 28,35mm, respectivamente. Altura e largura médias do CI foram, respectivamente, 2,08mm e 3,91mm. As médias da altura, largura e distância ao RIO do FI foram: 4,43mm, 5,18mm e 7,52mm, respectivamente. As distâncias médias do CASA ao rebordo alveolar foram: 18,54mm (CAN), 25,47mm (1PM), 28,43mm (2PM), 30,78mm (1M) e 33,21mm (2M); e do CASP: 22,3mm (1PM), 17,65mm (2PM), 15,34mm (1M) e 16,87mm (2M). As médias dos diâmetros do CASA e do CASP foram 0,90mm e 0,83mm, respectivamente, sendo que 77,5% dos CASA e 82% dos CASP eram &#x2264; 1mm e 22,5% dos CASA e 18% dos CASP eram entre 1-2 mm. Em relação ao seio maxilar, 53% e 44% dos CASA foram encontrados no terço superior e médio, respectivamente, e 64% e 36% dos CASP foram encontrados no terço inferior e médio, respectivamente. Houve diferença estatisticamente significativa (p<0,05) entre homens e mulheres para o comprimento, altura e largura do CI; para a altura, largura e distância ao RIO do FI; e para as distâncias dos CAS ao rebordo alveolar. CASA duplo, anastomose intra-óssea e extensão do CASA para a abertura piriforme foram detectados em 24,5%, 38,5% e 84% dos casos, respectivamente. A localização da anastomose foi teve maior ocorrência entre o CAN e 1PM (43%). Os resultados sugerem que a TCFC seja uma ferramenta adequada para examinar os CAS, CI e FI no planejamento de procedimentos cirúrgicos do terço médio da face, a fim de evitar danos a estruturas neurovasculares importantes. / To provide more information to clinicians in planning maxillofacial surgical interventions, the present study evaluated the presence, location and size of the superior alveolar canals (SAC), anterior (ASAC) and posterior (PSAC), infraorbital canal (IC) and infra-orbital foramen (IF) in cone beam computed tomography (CBCT) of 100 adult patients (&#x2265; 20 years old), obtained by i-CAT Classic®. One calibrated examiner observed SAC, IC and IF presence, bilaterally. When present, were measured: length (descending part, orbital floor part and total), width and height of the IC, height, width and distance from the IF to the inferior orbital rim (IOR), distance from the lower border of SAC to the alveolar crest in 5 regions: canine (CAN), first premolar (1PM), second premolar (2PM), first molar (1M) and second molar (2M); and the diameters of SAC. It was also observed the location of SAC in relation to the maxillary sinus floor and the presence of anatomical landmarks such as doble/multiple canal, intraosseous anastomosis and ASAC extension to the piriform aperture. Associations between men and women, right and left sides and regions were investigated for all measurements and presence using statistical methods separately. The presence of the IC and IF was 100%. The presence of ASAC/PSAC was: 99%/0% (CAN), 99%/21% (1PM), 89%/41% (2PM), 46%/44% (1M) e 7%/61% (2M). The mean lengths of the IC descending part, IC orbital floor part and total lenght of the IC were 8.82mm, 19.44mm and 28.35mm, respectively. The mean height and width of the IC were, respectively, 2.08mm and 3.91mm. The mean height, width and distance to the IOR of IF were: 4.43mm, 5.18mm and 7.52mm, respectively. The mean distances of ASAC to the alveolar crest were: 18.54mm (CAN), 25.47mm (1PM), 28.43mm (2PM), 30.78mm (1M) and 33.21mm (2M); and of PSAC: 22.3mm (1PM), 17.65mm (2PM) 15.34mm (1M) and 16.87mm (2M). The mean diameters of ASAC and PSAC were 0.90mm and 0.83mm, respectively, and that, 77.5% of ASAC and 82% of PSAC were &#x2264; 1mm and 22.5% of ASAC and 18% of PSAC were between 1-2 mm. In relation to the maxillary sinus, 53% e 44% of the ASAC were found in the upper and middle third of maxillary sinuses, respectively, and 64% and 36% of the PSAC were found in lower and middle third, respectively. There was a statistically significant difference (p<0.05) between men and women for the length, height and width of the IC, for the height, width and distance to the IOR of IF, and for distances of SAC to the alveolar crest. Double ASAC, intraosseous anastomosis and ASAC extension to the piriform aperture were present in: 24.5%, 38.5% and 84% of the cases, respectively. The location of the anastomosis had more incidence between the CAN and 1PM (43%). The results suggest that CBCT is a suitable tool to evaluate the SAC, IC and IF, assisting surgeons in planning surgical procedures of the midface, in order to avoid damage to important neurovascular structures.

A partir da teoria de resposta linear (formalismo de Kubo) calculamos a condutividade de spin $\\sigma_^$ para um gás bidimensional de elétrons formado num poço quântico com duas subbandas devido a atuação de um novo tipo de interação spin-órbita [Bernardes et al. \\textit{Phys. Rev. Lett.} \\textbf, 076603 (2007) \\& Calsaverini \\textit{et al}. \\textit{Phys. Rev. B} \\textbf, 155313 (2008)]. Este novo termo é não-nulo mesmo em estruturas simétricas e surge devido ao acoplamento entre os estados confinados no poço de paridades diferentes. Encontramos um valor para $\\sigma_^$ não-nulo e não-universal (dependente da intensidade do acoplamento $\\eta$) quando somente uma das subbandas está ocupada, ao contrário de Rashba. Para encontrarmos valores realistas para $\\sigma_^$, determinamos $\\eta$ via cálculo autoconsistente. Esse cálculo é executado para diferentes valores de densidade eletrônica em poços simples e duplos. Obtivemos que $\\sigma_^$ possui um comportamento não-monótono e sofre inversão de sinal como função da energia de Fermi (densidade de elétrons) conforme ela varia entre as duas subbandas. Contudo nossos resultados indicam que a condutividade Hall de spin é muito pequena $\\left(``\\ll \\frac{8\\pi}\"ight)$ nesses sistemas (poços simples e duplos) e possivelmente não mensurável. / Using the Kubo linear response theory, we investigate spin Hall conductivity $\\sigma_^$ in a two-dimensional electron gas in quantum wells with two subbands, when intersubband-induced spin-orbit coupling is operative [Bernardes et al. \\textit{Phys. Rev. Lett.} \\textbf, 076603 (2007) \\& Calsaverini \\textit{et al}. \\textit{Phys. Rev. B} \\textbf, 155313 (2008)]. This new spin-orbit term is non-zero even in symmetric structures and it arises from the distinct parity of the confined states. We find non-zero and non-universal $\\sigma_^$ (dependent on spin-orbit coupling strength $\\eta$) when only one of the subbands is occupied. This is in contrast to the Rashba spin-orbit interaction for which $\\sigma_^$ is identically zero. To obtain realistic values for $\\sigma_^$, we develop a self-consistent scheme to calculate $\\eta$. We performed this calcultion for different values of the eletronic density in single and double wells. We find that $\\sigma_^$ shows a non-monotonic behavior and a sign change as the Fermi energy (carrier density) varies between the two subband edges. However, our results indicate that $\\sigma_^$ is extremely small $\\left(``\\ll \\frac{8\\pi}\"ight)$ and possibly not measurable.

OBJETIVO: avaliar a capacidade de índices de preenchimento muscular da órbita, calculados a partir de medidas na tomografia computadorizada de multidetectores, detectar a neuropatia óptica distireoidiana em pacientes com orbitopatia de Graves. MÉTODOS: noventa e três pacientes com diagnóstico de orbitopatia de Graves foram prospectivamente estudados. Todos os pacientes foram submetidos a um exame oftalmológico completo e à tomografia computadorizada de multidetectores. Na estação de trabalho do tomógrafo foram calculados índices baseados em medidas lineares, de área e de volume de preenchimento muscular da órbita. O índice linear de Barrett, foi calculado a partir da relação entre a medida dos músculos extra-oculares em cortes coronais no ponto médio do nervo óptico orbitário e o diâmetro da órbita na mesma posição. Nesse mesmo corte coronal uma escala de 0 a 3 foi utilizada para categorizar o grau do preenchimento muscular e de compressão do nervo óptico segundo método descrito por Nugent e colaboradores. Medidas de área foram realizadas de cortes coronais a 12, 18 e 24 mm da linha interzigomática. Três índices de área foram calculados estimando-se a razão entre a área dos músculos extraoculares e a do continente ósseo medidas. Herniação de gordura orbitária pela fissura orbitária superior foi registrada como presente ou ausente conforme método descrito por Birchall e colaboradores. Dois índices volumétricos foram calculados, o primeiro baseado em cortes axiais de todo o continente orbitário (do ápice à rima orbitária anterior) e o segundo baseado em cortes coronais da órbita a partir de um ponto médio do segmento orbitário do nervo óptico até o limite anterior do canal óptico. As órbitas foram divididas em dois grupos, um com e outro sem neuropatia óptica distireoidiana e esses grupos foram comparados entre si. RESULTADOS: cento e duas órbitas de 61 pacientes atenderam aos critérios de inclusão e foram analisadas. Quarenta e uma órbitas eram do grupo com neuropatia e 60 daquele sem a neuropatia óptica distireoidiana. Para todos os índices, exceto para o de herniação de gordura, houve diferença significativa entre os dois grupos (<0,001). A melhor combinação de sensibilidade e especificidade para o índice linear de Barrett foi de 79% e 72% respectivamente, com razão de chances de 9.2. A escala categórica de Nugent apresentou sensibilidade de 58,3% e especificidade de 84,7%, acurácia de 74,7% e razão de chances de 7,8. Todos os índices de área e de volume apresentaram boa capacidade na detecção da neuropatia óptica distireoidiana. Os índices com melhor desempenho diagnóstico foram o de área a 18mm com sensibilidade de 91,7%, especificidade de 89,9%, acurácia de 90,5% e razão de chance de 97,2, e o de volume do ápice orbitário com sensibilidade de 92%, especificidade de 86%, acurácia de 88% e razão de chance de 97,2. CONCLUSÕES: os novos índices calculados baseados em área e volume foram preditores da neuropatia óptica e apresentaram desempenho superior aos métodos reproduzidos de estudos anteriores. A continuidade dos estudos na busca de métodos objetivos e capazes de identificar a neuropatia óptica distireoidiana com cada vez maior eficiência e praticidade é de grande relevância para a melhoria do diagnóstico e do tratamento da orbitopatia de Graves e suas complicações / PURPOSE: to evaluate the ability of orbital apex crowding indexes, calculated with multidetector-computed tomography (MDCT), to detect dysthyroid optic neuropathy (DON). METHODS: ninety-three patients with GO were studied prospectively with complete neuro-ophthalmic examination and MDCT scanning. All patients underwent a complete neuro-ophthalmic examination and scanning on a MDCT. In a dedicated workstation, linear, square and volumetric indexes of the orbital apex crowding were calculated. Barretts linear index was calculated as the percentage of the orbit occupied by muscles in a coronal scan halfway between the posterior globe and the orbital apex. At the same coronal scan, the severity of optic nerve crowding was also assessed by using the subjective grading scale (0, 1, 2 or 3) described by Nugent et al. Quantitative square area measurements were performed on coronal sections 12, 18 and 24 mm from the interzygomatic line. The muscular/bony area ratio was calculated as a crowding index. Intracranial fat prolapse through the superior orbital fissure was recorded as present or absent, according to a method described Birchall at al. Two volumetric indexes were calculated, one from axial scans of the entire orbit content (up to the orbital rim) and one from coronal scans of the orbital content from the entrance of the optic canal up to the middle point of the orbital segment of the optic nerve. Orbits were divided into two groups: with or without DON and comparison between groups was performed. RESULTS: one hundred and two orbits (41 orbits with DON, and 61 without DON) of 61 patients met the inclusion criteria and were included in the analysis. All indexes, except the intracranial fat prolapse, were significantly greater in orbits with DON (<0,001). There was no significant difference regarding intracranial fat prolapse. Area under the receiver operating characteristics curves was 0.91, 0.93 and 0.87 for CIs at 12, 18 and 24 mm, respectively. The best combination of sensitivity and specificity for the Barretts index was 79%/72% and odds ratio of 9.2. The Nugents subjective grading scale detected DON with 58.3% sensitivity, 84,7% specificity, 74.7% accuracy and odds ratio 7.8. All square area and volumetric indexes calculated presented good ability to detect DON. The best performance of the square area indexes was observed at 18 mm where a cutoff value of 57.5% showed sensitivity of 91.7% and a specificity of 89.8%, accuracy 90.5% and odds ratio of 97.2. The best sensitivity/specificity ratio of the volumetric indexes was found for the one calculated at the apex, with sensitivity of 93%, specificity of 84%, and accuracy of 88% for detecting DON. CONCLUSIONS: The new orbital crowding indexes based on area and volumetric measurements found to predict DON more reliably than Barretts linear index, subjective grading of orbital crowding or intracranial fat prolapse. Further imaging studies would be useful to validate and improve objective methods to predict DON, and thus contribute to early diagnosis treatment

Cette thèse est dédiée à l'étude théorique de phases exotiques dans un gaz dilué de bosons avec deux composantes (spins) en présence d'un couplage spin-orbite (SOC) entre ces deux états internes. En ajoutant ce dernier couplage à une description de type champs classiques de notre système, nous montrons que cette méthode permet de prédire le diagramme de phase à température finie de manière quantitative, efficace et fiable. Notre étude porte particulièrement sur un système de bosons bidimensionnels avec SOC dont nous dessinons le diagramme de phase en fonction de l'anisotropie du couplage spin-orbite ainsi que des interactions. Dans le cas d'un SOC anisotrope, une transition de phase de type Berenzinskii-Kosterlitz-Thouless sépare une phase dite normale d'une phase superfluide à plus basse température. L'ordre des spins du quasi-condensat dans la phase superfluide est alors guidé par les interactions de contact dépendantes du spin. Elles favorisent l'apparition soit d'un état onde plane avec moment non-nul (PW) soit d'une superposition linéaire de deux ondes planes appelée état de bande (SP). Pour des interactions indépendantes du spin des particules, nos simulations indiquent une fractionalisation du quasi-condensat. Les états PW et SP restent alors dégénérés. Dans le cas d'un SOC isotrope, nos calculs n'indiquent aucune transition de phase à la limite thermodynamique et à température finie. Un changement de comportement non critique subsiste pour un nombre important mais fini d'atomes. / In this thesis, we theoretically study the occurrence of exotic phases in a dilute two component (spin) Bose gas with artificial spin-orbit coupling (SOC) between the two internal states. Including spin-orbit coupling in classical field Monte Carlo calculations, we show that this method can be used for reliable, quantitative predictions of the finite temperature phase diagram. In particular, we have focused on SOCed bosons in two spatial dimensions and established the phase diagram for isotropic and anisotropic SOC and interparticle interactions. In the case of anisotropic SOC, the system undergoes a Berenzinskii-Kosterlitz-Thouless transition from a normal to a superfluid state at low temperature. The spin order of the quasicondensate in the low temperature superfluid phase is driven by the spin dependence of the interparticle interaction, favoring either the occurence of a single plane wave state at non-vanishing momentum (PW) or a linear sperposition of two plane waves with opposite momenta, called stripe phase (SP). For spin-independent interparticle interaction, our simulations indicate a fractionalized quasicondensate where PW and SP remain degenerate. For isotropic SOC, our calculations indicate that no true phase transition at finite temperature occurs in the thermodynamic limit, but a cross-over behavior remains visible for large, but finite number of atoms.

In the terahertz (THz) band, high-harmonic operations of gyro-devices are attractive for the great potential to reduce the required external magnetic field strength, which is proportional to the oscillation frequency but inversely proportional to the operational harmonics. This thesis focuses on the study of high-harmonic operation of the gyro-devices. Specifically, a high-harmonic large-orbit gyrotron (LOG) and the output system for a gyro-multiplier will be investigated. Firstly, the complex-cavity gyrotron, which is the foundation of the gyro-multiplier scheme, is studied by programming and computer simulation. The computer code and the complex-cavity operation are then verified by three-dimensional (3D) Particle-In-Cell (PIC) simulation. The code can be used as a preliminary design tool of the beam-wave interaction cavity for both the LOG and the gyro-multiplier. Secondly, a high-harmonic LOG operating with the TEm,1,1 modes (m=4-9) has been designed and investigated. It is shown that by proper choice of the operation parameters, selective excitation of oscillation from the fourth to the ninth harmonic of the electron cyclotron resonance can be achieved with kW-level output power from 230 GHz to 465 GHz. By enabling the high-harmonics operation, the required external magnetic field strengths are reduced to the range between 2.6 T to 3.1 T. The parameter variation study is also performed to provide a general conclusion of the high-harmonic LOGs operation. Thirdly, this thesis presents the investigation of a quasi-optical output system for a fourth-harmonic gyro-multiplier in the THz band. A dual-harmonic quasi-optical mode converter (DQMC) and a frequency selective surface (FSS) are employed within this system. It is shown that the optimal design of the DQMC requires a special mode selection in the gyro-multiplier. The high-pass FSS is designed, fabricated and experimentally verified by a THz-TDS system. It is demonstrated that the designed FSS is capable of handling the high-power output from the gyro-multiplier.

<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>