Recent advances in the chemical vapor deposition method of growing graphene sheets suggest that graphene rings can grow. We may anticipate that chemical methods can be developed to construct twisted nano-ribbons to form Möbius structures in the very near future. I investigated the quantum mechanics of an electron constrained to motion on a nanoscale Möbius ring by solving the Schrdinger equation on the curved surface. The close analogy between ordinary cylindrical rings and Möbius rings is displayed by the closeness of their energy spectra. The expectation values for the angular momentum component L_z are shown to be close, but not exactly equal, to integral or half-integral multiples of hbar. The half-integer angular momentum states are present only for the nontrivial topology of Möbius rings. The effect of the curvature of the Möbius rings manifests itself in the level splitting. This can be understood in terms of representations of the discrete rotational groups C_nv. The nonzero variance of L_z will allow weak transitions between integral and half-integral angular momentum states, while preserving the unit angular momentum for photons. Again, since the topology of the system is critical for the Aharonov-Bohm effect, I investigated the AB effect on Möbius rings and found a remarkable pattern in transmission through finite-width 2D ring structures with finite-width input and output contacts attached at the periphery. The periodicity in the magnetic flux, in units of h/e, is weakly broken on 2D rings of finite width. The unusual states with half-integer values of observed on Möbius rings, investigated earlier, display a different characteristic in transmission. In view of the fascinating properties displayed by the non-trivial topology in terms of its novel two-dimensional physics, we expect that the properties of carriers on the Möbius ring that we have presented here will be relevant for practical applications.

Three-dimensional (3D) displays project 3D images that give 3D perceptions and mimic real-world objects. Among the rich varieties of 3D displays, multiview displays take advantage of light’s various degrees of freedom and provide some of the 3D perceptions by projecting 2D subsampling of a 3D object. More 2D subsampling is required to project images with smoother parallax and more realistic sensation. As an additional degree of freedom with theoretically unlimited state space, orbital angular momentum (OAM) modes may be an alternative to the conventional multiview approaches and potentially project more images. This research involves exploring the possibility of encoding/decoding off-axis points in 2D images with OAM modes, development of the optical system, and design and development of a multiview colour display architecture. The first part of the research is exploring encoding/decoding off-axis points with OAM modes. Conventionally OAM modes are used to encode/decode the on-axis information only. Analysis of on-axis OAM beams referenced to off-axis points suggests representation of off-axis displacements as a set of expanded OAM components. At current stage off-axis points within an effective coding area are possible to be encoded/decoded with chosen OAM modes for multiplexing. Experimentally a 2D image is encoded/decoded with an OAM modes. When the encoding/decoding OAM modes match, the image is reconstructed. On the other hand, a dark region with zero intensity is shown. The dark region suggests the effective coding area for multiplexing. The final part of the research develops a multiview colour display. Based on understandings of off-axis representation of a set of different OAM components and experimental test of the optical system, three 1 mm monochromatic images are encoded, multiplexed and projected. Having studied wavelength effects on OAM coding, the initial architecture is updated to a scalable colour display consisting of four wavelengths.

Em vista de recentes determinações experimentais do perfil de Compton (Eisenberger, Phys. Rev., A2, 1678(1970); Wellenstein e Bonham, Phys. Rev., A7, 1568(1973}, procuramos efetuar um estudo comparativo de cálculos teóricos do perfil de Compton para o átomo de hélio (1S). Para tal, o conjunto de funções de onda elaboradas por Shull e L6wdin (J.Chem.Phy., 23, 1362(1955); 23, 1565(1955}; 30, 617(1959} mostrou-se bastante adequado, visto que permitiu observar a influência da função de onda no cálculo de perfil de Compton. Nossos resultados mostram em contraste à idéia geralmente aceita, que mesmo funções de onda igualmente boas para o cálculo da energia podem fornecer perfis de Compton com um erro maior que o experimental. Alem disso, apresentamos um conjunto de novos dados para o perfil de Compton e para a distribuição radial de momentum. Procuramos, também explicar essas discrepâncias relacionando-as com a transformada de Fourier da função de onda no espaço de configuração. / In view of the recent experimental determination of the Compton profile (Eisenberger, Phys., Rev., A2,1678(1970); Wellenstein and Bonham, Phys, Rev., A7, 1568(1973), we have performed a comparative study of theoretical calcu1ation of the Compton profile for the helium atom (1S). For such, the set of wave functions elaborated by Shull and Löwdin (J.Chem. Phys., 23, 1362(1955); 23, 1565(1955); 30, 617(1959) show itself specially suftable since it was possible to observe the influence af the wave functions on the calculated profile. Our results show in, contrast to general accepted idea, that even equally good wave functions in the energy sense may give theoretical profiles in error greater than the experimental one. Besides, we have presented a set of new data for the Compton profile and radial momentum distribution. A1so we have tried to explain the source of these discrepancies relating them to the Fourier transformation of the wave function in the configuration space.

Dans le Modèle Standard de la physique des particules, la théorie de l’interaction forte, la chromodynamique quantique (QCD), est une théorie de jauge de groupe de symétrie SU (Nc) par rapport au nombre quantique de couleur. QCD obéit à la propriété de liberté asymptotique, permettant le calcul d’observables physiques à haute énergie en utilisant la QCD perturbative (pQCD). Cette thèse traite de la description en pQCD des taux de production de hadrons dans les collisions hadroniques à haute énergie, en vue d’applications à la phénoménologie des collisions proton-noyau et noyau-noyau dans les collisionneurs de hadrons (RHIC, LHC), où des effets nucléaires (shadowing, perte d’énergie partonique, élargissement de l’impulsion transverse) entrent en jeu. Dans une première partie, j’étudie l’élargissement de l’impulsion transverse d’un système de partons énergétiques traversant un noyau, en mettant l’accent sur la structure de couleur du processus. Un cadre théorique basé sur le formalisme des dipôles est utilisé, et une équation cinétique est dérivée pour la distribution en impulsion transverse de la paire de partons, en demandant que cette paire soit dans un état de couleur donné (représentation irréductible de SU (Nc)) à la fois dans l’état initial et dans l’état final. La structure de couleur est codée dans un opérateur d’évolution de couleur, qui est obtenu pour tout type de paire de partons. Pour une paire compacte de petite taille, la dérivation donne une interprétation physique claire du processus d’élargissement de l’impulsion transverse. Dans une deuxième partie, je discute la matrice de dimension anormale Q, qui est formellement analogue à l’opérateur d’évolution précédent, et qui apparaît lors de l’ étude du rayonnement de gluons mous associé à une diffusion partonique dure 2 −> 2. Il a été remarqué que la matrice Q associée à gg −> gg a une symétrie surprenante (reliant les degrés de liberté externe et interne). J’ai développé des outils pour dériver les matrices Q associées à des diffusions 2 −> 2 impliquant des partons généralisés, afin d’explorer si la symétrie observée pour gg −> gg est fortuite ou non. / In the Standard Model of particle physics,the theory of the strong interaction, Quantum Chromodynamics (QCD), is a gauge theory of symmetry group SU (Nc) with respect to the color quantum number. QCD obeys the property of asymptotic freedom, allowing the computation of high-energy physical observables using perturbative QCD (pQCD). This thesis deals with the pQCD description of hadron production rates in high-energy hadronic collisions, in view of applications to the phenomenology of proton-nucleus and nucleus-nucleus collisions at hadron colliders (RHIC,LHC), where so-called nuclear effects (shadowing, parton energy loss, transverse momentum broadening) come into play. In a first part, I study the transverse broadening of an energetic parton system crossing a nucleus, putting emphasis on the color structure of the process. A theoretical setup based on the dipole formalism is used,and a kinetic equation is derived for the parton pair transverse momentum distribution, requiring the parton pair to be in a given color state (SU (Nc) irreducible representation) both in the initial and final state. The color structure is encoded in a color evolution operator, which is obtained for any type of parton pair. For a small-size compact pair, the derivation yields a transparent physical interpretation of the pair transverse broadening process. In a second part, I discuss the soft anomalous dimension matrix Q, which is formally analogous to the previous evolution operator, and which appears when studying soft gluon radiation associated to 2 −> 2 hard parton scattering. It has been noticed that the Q-matrix associated to gg −> gg has a surprising symmetry (relating external and internal degrees of freedom). I developed tools to derive the Q-matrices associated to2 −> 2 scatterings involving generalized partons, in order to explore if the symmetry observed for gg −> gg is fortuitous or not.

Momentos de quadrupólo elétricos de estados isoméricos nucleares com vidas médias entre 10 nanosegundos e 100 milisegundos podem ser medidos com o método Espectroscopia de Mistura de Níveis (Level Mixing Spectroscopy- LEMS), utilizando campos magnéticos variáveis aplicados em núcleos implantados em materiais hospedeiros que possuam gradientes de campo elétrico. O Campo magnético externo pode ser substituido pelo campo hiperfino de materiais ferromagnéticos e sua variação poderia ser controlada variando a temperatura. O objetivo deste trabalho é verificar a viabilidade desta substituição. Implementamos o método LEMS no Laboratório Pelletron usando como caso teste o estado isomérico de 398 KeV do 69Ge que possui todas as suas propriedades nucleares conhecidas (meia vida, spin, momento magnético, momento de quadrupolo elétrico). Ele foi produzido pela reação 56Fe(16O, 2pn)69Ge com o feixe de 16O à 53 MeV (LAB) de energia, e depois implantado em Gadolínio que é ferromagnético abaixo de Tc = 289K. Medimos a anisotropia da radiação gama emitida por esse núcleo em função da temperatura. A comparação entre as medidas da anisotropia em função da temperatura, com medidas da anisotropia em função do campo magnético externo, feita pelo grupo de Leuven/Bélgica, nos levou a duas interpretações possíveis. Na primeira, supondo a interação elétrica constante e independente da temperatura, obtemos um campo magnético hiperfino anômalo para o Gd. Na segunda análise, obtivemos o campo hiperfino variando linearmente com a magnetização, admitindo gradientes de campo elétrico dependentes da temperatura. Medidas futuras usando monocristal de Gd poderão resolver esta ambiguidade, bem como medidas TDPAD (Time Diferencial Perturbed Angular Distribuition) em função da temperatura, na qual se mede diretamente o campo hiperfino. / The Level Mixing Spectroscopy method allows to measure the eletric quadrupole moments of high spin isomeric nuclear states (10ns < t < 100ms) produced in nuclear reactions. The magnetic interaction is usualy created by an intense external magnetic field. The eletric quadrupole interaction can be created by recoi-implantation of the nuclei in non-cub crystals, used as hosts. The external magnetic field can then be replaced by the hiperfine fields of ferromagnetic materials, controling its intensity by temperature variation. The purpose of the research performed for this work is to verify the viability of this replacement. We adapt the LEMS method to be used in the Pelletron Laboratory. We choose the isomeric state at 398 KeV exitation energy in the 69Ge nucleus as a test case, because it has all nuclear properties well known (half-life, spin, magnetic moment, eletric quadrupole moment). It was produced by the 56Fe(16O, 2pn)69Ge reaction, with a 16O beam at 53 MeV, and implanted and stopped in a Gadolinium host, which is a ferromagnet from low temperatures up to Tc=289 K. We measure the anisotropy of the emitted gama ray as a function of the temperature of the host. The comparison of this measurement with another of the anisotropy as a function of an external magnetic field strength, done by the Leuven/Belgium group, show us two possibilities. In the first, we suppose that the eletric interaction is cosntant and independent of temprature and we obtain an anomalous magnetic hyperfine field for Gd. In the second one, we obtain a hyperfine field that follows the magnetization if we assume eletric field gradientes that are temperature dependent. New measurements by using Gd monocrystal and the TDPAD (Time Diferencial Perturbed Angular Distribution) method may solve this ambiguity.

Imaging at the nanoscale and/or at remote locations holds great promise for studies in fields as disparate as the life sciences and materials sciences. One such microscopy technique, stimulated emission depletion (STED) microscopy, is one of several fluorescence based imaging techniques that offers resolution beyond the diffraction-limit. All current implementations of STED microscopy, however, involve the use of free-space beam shaping devices to achieve the Gaussian- and donut-shaped Orbital Angular Momentum (OAM) carrying beams at the desired colors –-- a challenging prospect from the standpoint of device assembly and mechanical stability during operation. A fiber-based solution could address these engineering challenges, and perhaps more interestingly, it may facilitate endoscopic implementation of in vivo STED imaging, a prospect that has thus far not been realized because optical fibers were previously considered to be incapable of transmitting the OAM beams that are necessary for STED. In this thesis, we investigate fiber-based STED systems to enable endoscopic nanoscale imaging. We discuss the design and characteristics of a novel class of fibers supporting and stably propagating Gaussian and OAM modes. Optimization of the design parameters leads to stable excitation and depletion beams propagating in the same fiber in the visible spectral range, for the first time, with high efficiency (>99%) and mode purity (>98%). Using the fabricated vortex fiber, we demonstrate an all-fiber STED system with modes that are tolerant to perturbations, and we obtain naturally self-aligned PSFs for the excitation and depletion beams. Initial experiments of STED imaging using our device yields a 4-fold improvement in lateral resolution compared to confocal imaging. In an experiment in parallel, we show the means of using q-plates as free-space mode converters that yield alignment tolerant STED microscopy systems at wavelengths covering the entire visible spectrum, and hence dyes of interest in such imaging schematics. Our study indicates that the vortex fiber is capable of providing an all-fiber platform for STED systems, and for other imaging systems where the exploitation of spatio-spectral beam shaping is required.

In communication and family studies, narrative inheritance Òprovides us with a framework for understanding our identity throughÓ the stories of those who preceded us in our families (Goodall, 2005, p. 497). Ballard and Ballard (2011) supplement the concept of narrative inheritance with the idea of Ònarrative momentum,Ó suggesting that family identity moves forward into the future through the narratives the family tells (p. 80). In this account, I question the hegemony of both concepts, particularly narrative momentum which discounts the variety of family types, while supporting the dominant cultural discourses of what defines Òfamily.Ó

This thesis encompasses a body of experimental work on the use of structured light in quantum cryptographic protocols. In particular, we investigate the ability to perform quantum key distribution through various quantum channels (fibre, free-space, underwater) in laboratory and realistic conditions. We first demonstrate that a special type of optical fibre (vortex fibre) capable of coherently transmitting vector vortex modes is a viable quantum channel. Next, we describe the first demonstration of high-dimensional quantum cryptography using structured photons in an urban setting. In particular, the prevalence of atmospheric turbulence can introduce many errors to a transmitted key; however, we are still able to transmit more information per carrier using a 4-dimensional scheme in comparison to a 2-dimensional one. Lastly, we investigate the possibility of performing secure quantum communication with twisted photons in an uncontrolled underwater channel. We find that though it is possible for low-dimensional schemes, high-dimensional schemes suffer from underwater turbulence without the use of corrective wavefront techniques.

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler's equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics.

This dissertation contains two essays. The first essay investigates the measure of FX liquidity and determinants of the change in FX liquidity. Using 20 cross currency exchange rates over spanning period of 1999 to 2016, funding constraints and global risks are responsible for the main drivers of changing in FX liquidity. The magnitudes of both G7 and emerging volatility index are offsetting each other in all the regression models indicating that FX investors take diversification trading strategies to diversify their portfolios. The financial crisis provides an evidence that the more financial constraint issues contribute to the change in FX market illiquidity more than non-financial crisis period. Extending to liquidity predictability, I find, however, that the lag of market FX liquidity is responsible for the change in FX liquidity than any other explanatory variables My second essay investigates the momentum returns of U.S. equities by presenting comprehensive approaches. Traditionally, momentum portfolios are constructed by ranking based on excess returns. Using this sorting technique, I confirm that there is a presence of momentum returns in U.S. equities for all of the 48 industries. The results also indicate that the portfolios that are sorted by idiosyncratic volatility as well as by diversification strategy cannot achieve the highest returns as for sorting based on excess returns. Further, I examine the momentum portfolio predictability using the inverse conditional volatility proposed by Moreira and Muir (2017), and show that the momentum returns are affected by the size of liquidity and the risk factors rather than by the economic variables.