Recently there is an increase in interest in the Moon as a destination for space missions. This increased interest is in the composition and geography of the Moon as well as using the Moon to travel beyond the Earth to other planets in the solar system. This thesis explores the mechanics behind a lunar mission and the costs and benefits of different approaches. To constrain this problem, the launch criteria are those of Wallops Flight Facility (WFF), which has expressed interest in launching small spacecraft to the Moon for exploration and study of the lunar surface. The flight from the Earth to the Moon and subsequent lunar orbits, referred to hereafter as the mission, is broken up into three different phases: first the launch and parking orbit around the Earth, second the transfer orbit, and finally the lunar capture and orbit. A launch from WFF constrains the direction of the launch and the possible initial parking orbits. Recently WFF has been offered the use of a Taurus XL launch vehicle whose specifications will be used for all other limitations of the launch and initial parking orbit. The orbit investigated in this part of the mission is a simple circular orbit with limited disturbances. These disturbances are only a major factor for long duration orbits and don't affect the parking orbit significantly. The transfer orbit from the Earth to the Moon is the most complex and interesting part of the mission. To fully describe the dynamics of the Earth-Moon system a three-body model is used. The model is a restricted three-body problem keeping the Earth and Moon orbiting circularly around the system barycenter. This model allows the spacecraft to experience the influence of the Earth and Moon during the entire transfer orbit, making the simulation more closely related to what will actually happen rather than what a patched conic solution would give. This trajectory is examined using Newtonian, Lagrangian, and Hamiltonian mechanics along with using a rotating and non-rotating frame of reference for the equations of motion. The objective of the transfer orbit is to reduce the time and fuel cost of the mission as well as allow for various insertion angles to the Moon. The final phase of the mission is the lunar orbit and the analysis also uses a simple two body model similar to the parking orbit. The analysis investigates how the orbits around the Moon evolve and decay and explores more than just circular orbits, but orbits with different eccentricities. The non-uniform lunar gravity field is investigated to accurately model the lunar orbit. These factors give a proper simulation of what happens to the craft for the duration of the lunar orbit. Tracking the changes in the orbit gives a description of where it will be and how much of the lunar surface it can observe without any active changes to the orbit. The analysis allows for either pursuing a long duration sustained orbit or a more interesting orbit that covers more of the lunar surface. These three phases are numerically simulated using MATLAB, which is a focus of this thesis. In all parts of the mission the simulations are refined and optimized to reduce the time of the simulation. Also this refinement gives a more accurate portrayal of what would really happen in orbit. This reduction in time is necessary to allow for many different orbits and scenarios to be investigated without using an unreasonable amount of time. / Master of Science

Achieving the quantum control of ever more complex systems has been a driving force of atomic, molecular, and optical physics. This goal has materialized in the harnessing of systems with increasingly rich structures and interactions: the more sophisticated the system, the more faceted and fascinating its application to fields as varied as quantum simulation, quantum information, many body physics, metrology, and quantum chemistry. One of the current frontiers of quantum control is ultracold dipolar molecules. They present rich internal structures and long-range, anisotropic dipole-dipole interactions which promise to revolutionize AMO physics, for example by realizing realistic Hamiltonians in quantum simulation, by providing a new platform for quantum information, and by achieving a novel kind of quantum liquid. Despite its promises, the full quantum control of dipolar molecules has been over a decade in the making. The difficulties in either directly laser cooling molecules or in collisionally stabilizing their bulk samples have been major roadblocks that have hampered the development of this quantum system. The realization of a Bose-Einstein condensate of dipolar molecules has been a particularly elusive milestone. In this thesis, I report on the first observation of this quantum state of matter. The work that brought us to this achievement parallels the historical evolution of AMO physics in the last thirty years. To reach a BEC of molecules, we initially constructed a dual species experiment capable of realizing the simultaneous Bose-Einstein condensation of atomic sodium (Na) and cesium (Cs). Individual BECs of sodium and cesium were first reported in 1995 and 2003 respectively, while our experiment was the first instance of their concurrent condensation. The study of the Na-Cs interatomic scattering properties in an homogeneous magnetic field showed us the path to the Feshbach association of loosely-bound sodium-cesium (NaCs) molecules, a technique first demonstrated in 2006 for heteronuclear molecules but never attempted on our species. Following the Feschbach association, we determined a novel pathway to the molecular electronic, vibrational and rotational ground state using STIRAP. From this point, we found ourselves at the forefront of the field: bulk samples of bosonic molecules such as NaCs had neither been stabilized against collisional losses nor evaporatively cooled. At first, we successfully applied a single-frequency microwave shielding approach to decrease in-bulk losses by a factor of 200 and reach lifetimes on the order of 2 s, allowing us to measure high elastic scattering rates and characterize their dipolar anisotropy. Moreover, we demonstrated the first evaporative cooling of a bosonic molecular gas by increasing its phase-spacedensity by a factor of 20 and reaching a temperature of 36(5) nK. Since this proved insufficient to achieve Bose-Einstein condensation due to unexpected three-body losses, we introduced an enhanced microwave shielding technique, double microwave shielding. This further decreased loss rates enabling efficient evaporative cooling of our sample to a long-lived Bose-Einstein condensate of dipolar molecules. This new double microwave shielding technique also allows the tunability of the strength of dipole-dipole interaction, establishing ultracold bosonic dipolar molecules as a new quantum liquid for the exploration of many body physics. In addition to the experimental work on dipolar NaCs, we have theoretically explored the field of direct molecular laser cooling. Our aim was twofold: we aimed to expand the category of molecules that can be laser cooled and to simplify the identification of laser cycling schemes. For the former goal, we lifted the widespread assumption that only molecules with diagonal Franck-Condon factors could be laser cooled. For the latter, we decided to employ publicly available repositories of molecular transitions. A second consequence of the use of these databases is that they contain data on molecules of interest to other scientific fields, further establishing direct laser cooling as a technique that could be of interest beyond AMO physics. Our work was successful in that we identified laser cycling schemes for C₂ and OH+. To simplify the determination of laser cycling schemes, we developed a graph-based algorithm form their identification starting from spectroscopic data.

No description available.

We present a method of constructing the phase diagram at low temperatures, using the low temperature expansions. We consider spin Iattice systems described by a Hamiltonian with a d-dimensional perturbation space. We prove that there is a one-one correspondence between subsets of the phase diagram and extremal elements of some family of convex sets. We also solve a linear programming problem of the phase diagram for a set of affine functionals. / Ph. D.

In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm. / Ph. D. / incomplete_metadata

In this work, we investigate the spectrum of the non-relativistic Krönig-Penney Hamiltonian H_α= -d²/dx² +αΣ_m∈Zδ(-(2m+1)π) perturbed by a short-range potential λW and the spectrum of its relativistic counterpart obtained by replacing the Schrödinger Hamiltonian H_α with its relativistic analogue H̅_α. The interesting feature of both spectra is that they have gaps and that bound states may occur in such gaps as a consequence of the presence of the short-range potential representing the impurity. Such bound states, often called "impurity states" in the solid state physics literature. are important with regard to the conductivity properties of solids We show the existence of such bound states of H_α + λW in each sufficiently remote gap of its essential spectrum if the integral of W is different from zero and the 1 + 𝛅-moment of W is finite for some 𝛅 > 0. Furthermore, if the potential has a constant sign we prove that there is only one bound state in each sufficiently remote gap. We shall see that in the relativistic case one may have more than one bound state in each remote gap under the same assumptions on W. Nevertheless, we shall see that such additional bound states cannot appear in the range of energies of solid state physics. / Ph. D.

No description available.

Made available in DSpace on 2015-03-03T15:16:23Z (GMT). No. of bitstreams: 1 LeonardoM.pdf: 1880413 bytes, checksum: c785ee7cbc933eb3ac782dc9ac382e6c (MD5) Previous issue date: 2009-12-18 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / We use a tight-binding formulation to investigate the transmissivity and the currentvoltage (I_V) characteristics of sequences of double-strand DNA molecules. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare theresults for the genomic DNA sequence with those of arti_cial sequences (the long-range correlated Fibonacci and RudinShapiro one) and a random sequence, which is a kind of prototype of a short-range correlated system. The random sequence is presented here with the same _rst neighbors pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the transmissivity spectra, although the I_V curves seem to be mostly inuenced by the short-range correlations. We also analyze in this work the electronic and thermal properties along an _-helix sequence obtained from an _3 peptide which has the uni-dimensional sequence (Leu-Glu-Thr- Leu-Ala-Lys-Ala)3. An ab initio quantum chemical calculation procedure is used to obtain the highest occupied molecular orbital (HOMO) as well as their charge transfer integrals, when the _-helix sequence forms two di_erent variants with (the so-called 5Q variant) and without (the 7Q variant) _brous assemblies that can be observed by transmission electron microscopy. The di_erence between the two structures is that the 5Q (7Q) structure have Ala ! Gln substitution at the 5th (7th) position, respectively. We estimate theoretically the density of states as well as the electronic transmission spectra for the peptides using a tight-binding Hamiltonian model together with the Dyson's equation. Besides, we solve the time dependent Schrodinger equation to compute the spread of an initially localized wave-packet. We also compute the localization length in the _nite _-helix segment and the quantum especi_c heat. Keeping in mind that _brous protein can be associated with diseases, the important di_erences observed in the present vi electronic transport studies encourage us to suggest this method as a molecular diagnostic tool / Nesta tese, investigamos a transmissividade e as caracter?sticas de corrente como fun??o da diferen?a de potencial, no contexto da liga??o forte, em seq??ncias de dupla fita do DNA. Com o intuito de investigar a relev?ncia das correla??es subjacentes nas distribui??es dos nucleot?deos, comparamos os resultados de uma seq??ncia gen?mica do DNA com duas seq??ncias artificiais (Fibonacci e Rudin-Shapiro, que apresentam correla??o de longo alcance) e uma seq??ncia aleat?ria, prot?tipo de sistemas de correla??o de curto alcance. A seq??ncia aleat?ria utilizada apresenta a mesma correla??o de pares de primeiros vizinhos que a seq??ncia do DNA humano. Observamos que a caracter?stica de correla??o de longo alcance ? importante para o espectro de transmissividade, apesar das curvas IXV serem mais influenciadas por correla??es de curto alcance. Neste trabalho, analisamos tamb?m as propriedades t?rmicas e eletr?nicas de uma seq?encia α-h?lice, obtida de um pept?deo α3, o qual apresenta a seguinte seq??ncia unidimensional (Leu-Glu-Thr-Leu-Ala-Lys-Ala)3 (estrutura prim?ria). C?lculos ab initio qu?nticos s?o utilizados para obter as energias dos orbitais moleculares mais altos (HOMO, highest occupied molecular orbital), bem como suas integrais de transfer?ncias de cargas quando a seq??ncia α-h?lice forma uma estrutura fibrosa (variante 5Q) e n?o fibrosa (variante 7Q), as quais podem ser observadas atrav?s de microscopia eletr?nica de transmiss?o. A diferen?a entre as duas estruturas ? que a estrutura 5Q (7Q) apresenta a substitui??o Ala → Gln na 5a (7a) posi??o, respectivamente. N?s estimamos, teoricamente, a densidade de estado bem como o espectro de transmiss?o eletr?nico dos pept?deos, utilizando um Hamiltoniano no formalismo da liga??o-forte juntamente com a equa??o de Dyson. Al?m disso, n?s resolvemos a equa??o de Schr?dinger dependente do tempo para obter o espalhamento de um pacote de onda inicialmente localizado. N?s calculamos tamb?m o comprimento de localiza??o e, por fim, o calor espec?fico qu?ntico. Vale lembrar que a forma??o de prote?nas fibrosas podem estar associadas ? doen?as, de forma que as importantes diferen?as observadas no estudo das propriedades eletr?nicas de transporte nos encorajam a sugerir este m?todo como uma ferramenta de diagn?stico molecular

Cette thèse possède un double objectif : le premier est l'amélioration des techniques de contrôle en mécanique quantique, et plus particulièrement en RMN, grâce aux techniques du contrôle optimal géométrique. Le second consiste à étudier l'influence des singularités hamiltoniennes dans les systèmes physiques contrôlés. Le chapitre traitant du contrôle optimal étudie trois problèmes classiques en RMN : l'inversion simultanée de deux spins, l'inclusion des termes non-linéaires dans le modèle et la méthode du point fixe. Ensuite, nous appliquons le PMP au problème de transfert de population dans un système quantique à trois niveaux pour retrouver le processus STIRAP. Les deux chapitres suivants étudient les singularités hamiltoniennes. Nous montrons comment l'étude des singularités hamiltoniennes permet de contrôler la polarisation dans différentes fibres optiques. Ensuite, nous montrons l'existence d'une monodromie hamiltonienne généralisée dans le spectre vibrationnel de la molécule HOCl. Enfin, nous donnons une méthode de mesure de la monodromie hamiltonienne dynamique dans deux systèmes classiques en optique non-linéaire : le modèle de Bragg et le mélange à trois ondes / This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polarization in different type of optical fibers. Then, we show the existence of generalized hamiltonian monodromy in the vibrational spectrum of the HOCl molecule. Finally, we propose a method to measure dynamically the monodromy in two different nonlinear optics systems : the Bragg model and the three waves mixing model

Cremmer und Julia haben 1978 die Existenz von verborgenen En(n)-exzeptionellen Symmetrien in den maximalen Supergravitationstheorien (SUGRA), die aus der Kompaktifizierung der elfdimensionalen SUGRA auf einem n-Torus folgen, entdeckt. Die Existenz dieser En(n)-Symmetrien in den maximalen SUGRA ist eine ihrer bemerkenswertesten Eigenschaften, aber die Bedeutung dieser Symmetrien in der Quantentheorie ist noch nicht vollständig verstanden. Zudem ist erst seit 2013 bekannt, wie eine manifest En(n)-kovariante exzeptionelle Feldtheorie (ExFT), die auf einer exzeptionellen Geometrie basiert und insbesondere die elfdimensionale SUGRA beinhaltet, konstruiert werden kann (Hohm & Samtleben, 2013). In dieser Dissertation konstruieren wir die kanonische Formulierung der E6(6)-ExFT, was als Ausgangspunkt der kanonischen Quantisierung angesehen werden kann. Wir ermitteln die nicht-integrale Form des topologischen Terms der E6(6)-ExFT und untersuchen eine topologische Modelltheorie, die auf dem kinetischen Term der zwei-Form basiert. Um die Konstruktion einer verallgemeinerten Geometrie zu illustrieren konstruieren wir explizit den Y-Tensor für die Gruppe Sp(2n). Außerdem beschreiben wir eine vereinfachte kanonische Behandlung der Zwangsbedingungen des skalaren symmetrischen Raumes, welche wir für SL(n)/SO(n) erläutern. Zur Vorbereitung der kanonischen Analyse der ExFT untersuchen wir die kanonische Formulierung der manifest E6(6)-invarianten ungeeichten maximalen fünfdimensionalen SUGRA und führen eine umfassende kanonische Analyse, inklusive aller Eichtransformationen und der vollständigen Poisson-Algebra der Zwangsbedingungen, durch. Wir errechnen die Hamilton-Funktion der ExFT, sowie den Großteil der kanonischen (Eich-)Transformationen und Teile der Poisson-Algebra der Zwangsbedingungen. Zudem untersuchen wir, wie die kanonische Formulierung durch das verallgemeinerte Vielbein ausgedrückt werden kann und erörtern die mögliche Existenz von verallgemeinerten Ashtekar-Variablen. / In 1978 Cremmer and Julia discovered the existence of hidden non-compact global En(n) exceptional symmetries in the maximal supergravity (SUGRA) theories that follow from the compactification of eleven-dimensional SUGRA on an n-torus. The existence of these hidden exceptional symmetries in maximal SUGRA theories is one of their most notable features, but the role of these symmetries is not yet fully understood at the quantum level. Moreover it has only been known since 2013 how a manifestly En(n) covariant exceptional field theory (ExFT) can be constructed, which is based on an exceptional geometry and in particular contains the eleven-dimensional SUGRA (see Hohm & Samtleben, 2013). In this thesis we construct and investigate the canonical formulation of the (bosonic) E6(6) ExFT, which can be seen as the starting point of the canonical quantisation procedure. We calculate the explicit non-integral form of the topological term of the E6(6) ExFT and explore a topological model theory based on the two-form kinetic term. To illustrate the construction of a generalised geometry we explicitly construct the Y-tensor for the group Sp(2n). Furthermore we establish a simplified canonical treatment of the scalar coset constraints, which we illustrate for SL(n)/SO(n). As a preparation to the canonical analysis of the ExFT we calculate the canonical formulation of the manifestly E6(6) invariant ungauged maximal five-dimensional SUGRA theory and carry out a comprehensive canonical analysis including all gauge transformations and the full constraint algebra. We then proceed to work out the canonical formulation of the E6(6) ExFT. We calculate the full ExFT Hamiltonian, most of the canonical (gauge) transformations and parts of the constraint algebra. Moreover we examine how the canonical formulation can be expressed in the generalised vielbein form and we discuss the possible existence of generalised Ashtekar variables.