Ce travail s'attaque à la mise en évidence expérimentale d'effets quantiques dans le mouvement d'un résonateur mécanique macroscopique avec une masse effective de 33 microgrammes, soit 3 ordres de grandeur au-dessus de celle du système mécanique le plus massif observé à ce jour dans son état quantique fondamental. Nous avons conçu, fabriqué et fait fonctionner un résonateur optomécanique à 3,6 MHz avec une finesse optique de 100.000 et un facteur de qualité mécanique proche de 100 millions, inséré dans l'environnement à 100 mK d'un réfrigérateur à dilution. Nous présentons un montage optique complètement automatisé incluant une cavité de filtrage, une détection homodyne et plusieurs asservissements, implémentés dans un FPGA avec le programme PyRPL développé spécifiquement pour cette expérience. Nous avons refroidi par laser le mode de compression de notre résonateur mécanique jusqu'à un nombre moyen d'occupation thermique de 20 phonons. Le refroidissement est limité par l'apparition d'une instabilité optomécanique de plusieurs modes des suspensions, au-dessous de 100 kHz. Un filtre digital particulier pour supprimer cette instabilité nous a permis d'atteindre le régime où l'action en retour quantique contribue à hauteur d'environ 30 % au bruit de force total de l'oscillateur mécanique. Pour atteindre des contributions encore plus importantes à l'avenir, nous présentons la conception d'un miroir d'entrée à cristal phononique, caractérisé par un plancher de bruit de mouvement Brownien réduit. / In this work, we attempt the experimental demonstration of quantum effects in the motion of a macroscopic mechanical resonator with a mass of 33 micrograms, about 3 orders of magnitude above the mass of the heaviest system demonstrated so far in the quantum ground state. We have designed, fabricated, and operated an optomechanical resonator at 3.6 MHz, with an optical finesse of 100,000 and a mechanical quality factor near 100 million, embedded in the 100 mK environment of a dilution refrigerator. We present a fully automatized optical measurement setup, including a filter cavity, a homodyne detector, and various feedback controllers implemented in an FPGA with the custom-developed software PyRPL. We have laser-cooled the compression mode of our mechanical resonator to a mean thermal occupation number of 20 phonons. Cooling is limited by the onset of an optomechanical instability of suspension modes with frequencies below 100 kHz. A custom-tailored digital filter to suppress this instability has enabled us to reach a regime where quantum backaction amounts to about 30 % of the total force noise on the mechanical resonator. For even higher ratios in the future, we present the design of a phononic-crystal input mirror with a reduced Brownian motion displacement noise floor.

Made available in DSpace on 2015-05-15T11:46:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 695566 bytes, checksum: 26f7afc275ad83fa634352b9d522415e (MD5) Previous issue date: 2012-04-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we study the existence of two types of non-negative weak solutions for a class of problems of Schrodinger-Poisson type. This kind of problem models, for example, several physical phenomena in quantum mechanics. Initially, by minimization arguments, Splitting Lemma and the Variational Principle of Ekeland we find a weak solution that minimizes the minimum energy level associated to the variety of Nehari N. This is the so-called ground state solution. Afterwards we will find, by using the Linking Theorem, a strictly positive weak solution which is not a ground state solution: the so-called bound state solution. / Nesta dissertação, estudaremos a existência de dois tipos de soluções fracas não negativas para uma classe de problemas do tipo Schrödinger-Poisson, os quais modelam fenômenos físicos, por exemplo, em Mecânica Quântica. Inicialmente, encontraremos através de argumentos de minimização, do Lema Splitting e do Princípio Variacional de Ekeland, uma solução fraca que minimiza o nível de energia mínima associado a variedade de Nehari N. Tal solução é denominada do tipo ground state. Em seguida, encontraremos através do Teorema de Linking, uma solução fraca estritamente positiva que não é do tipo ground state. Tal solução é denominada do tipo bound state.

O caso finito de teorias topológicas de 1-gauge, quando nenhuma simetria global está presente, é bastante bem compreendido e classificado. Nos últimos anos, as tentativas de generalizar as teorias de 1-gauge através das chamadas teorias de 2-gauge abriram a porta para novos modelos interessantes e novas fases topológicas, as quais não são descritas pelos esquemas de classificação anteriores. Nesta tese, vamos além da construção de 2-gauge, e consideramos uma classe de modelos que vivem em maiores dimensões. Esses modelos estão inseridos em uma estrutura de complexos de cadeia de grupos abelianos, forçando a generalizar o conceito usual de configurações de gauge. A vantagem de tal abordagem é que, a ordem topológica fica manifestamente explcita. Isto é feito em ter- mos de uma cohomologia com coeficientes em um complexo de cadeia finita. Além disso, mostramos que a degenerescência do estado fundamental suporta um conjunto conve- niente de números quânticos que indexam os estados e que, além, foram completamente caracterizados. Consequentemente, nós também mostramos que muitos dos exemplos abelianos de teorias de 1 -gauge 2-gauge são recuperados como casos especiais desta construção. / The finite case of 1-gauge topological theories, when no global symmetries are present, is fairly well understood and classified. In recent years, attempts to generalize the latter situation through the so called 2-gauge theories have opened the door to interesting new models and new topological phases, not described by the previous schemes of classifica- tion. In this paper we go even beyond the 2-gauge construction by considering a class of models that live in arbitrary higher dimensions. These models are embedded in a structure of chain complexes of abelian groups, forcing to generalize the usual notion of gauge configurations. The advantage of such an approach is that, the topological order is explicitly manifest when the ground state space of these models is described. This is done in terms of a cohomology with coefficients in a finite chain complex. Furthermore, we show that the ground state degeneracy underpins a convenient set of quantum num- bers that label the states and that have been completely characterized. We also show that abelian examples of 1-gauge 2-gauge theories are recovered as special cases of this construction.

First-principles calculations such as density functional theory (DFT) employ numerical approaches to solve the Schrodinger equation of a system. Standard functionals employed to determine the cohesive system energy, specifically the local density and generalized gradient approximations (LDA and GGA), underestimate the correlation of 5f electrons to their ions in AO₂ systems (A=U/Pu/Np). The standard correction, the "Hubbard +U," causes the multidimensional energy surface to develop a large number of local minima which do not correspond to the ground state (global minimum). Because all useful energy values derived from DFT calculations depend on small differences between relatively large cohesive energies, comparing systems wherein one or more of the samples are not in the ground state has the potential to introduce large errors. This work presents an analysis of the fundamental issues of metastable states in both pure and binary AO₂ systems, investigates novel methods of handling them, and describes why current literature approaches which appear to work well for the pure compounds are not well-suited for systems containing multiple actinide species.

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first 'real' system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium. The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.

No description available.

Matter exists in many different phases, for example in solid state or in liquid phase. There are also phases in which the ordering of atoms is the same, but which differ in some other respect, for example ferromagnetic and paramagnetic states. According to Landau's symmetry breaking theory every phase transition is connected to a symmetry breaking process. A solid material has discrete translational symmetry, while liquid phase has continuous translational symmetry. But it has turned out that there also exist phase transitions that can occur without a symmetry breaking. This phenomenon is called topological order. In this thesis we consider one example of a theoretical model constructed on a two dimensional lattice in which one obtains topological order.

O caso finito de teorias topológicas de 1-gauge, quando nenhuma simetria global está presente, é bastante bem compreendido e classificado. Nos últimos anos, as tentativas de generalizar as teorias de 1-gauge através das chamadas teorias de 2-gauge abriram a porta para novos modelos interessantes e novas fases topológicas, as quais não são descritas pelos esquemas de classificação anteriores. Nesta tese, vamos além da construção de 2-gauge, e consideramos uma classe de modelos que vivem em maiores dimensões. Esses modelos estão inseridos em uma estrutura de complexos de cadeia de grupos abelianos, forçando a generalizar o conceito usual de configurações de gauge. A vantagem de tal abordagem é que, a ordem topológica fica manifestamente explcita. Isto é feito em ter- mos de uma cohomologia com coeficientes em um complexo de cadeia finita. Além disso, mostramos que a degenerescência do estado fundamental suporta um conjunto conve- niente de números quânticos que indexam os estados e que, além, foram completamente caracterizados. Consequentemente, nós também mostramos que muitos dos exemplos abelianos de teorias de 1 -gauge 2-gauge são recuperados como casos especiais desta construção. / The finite case of 1-gauge topological theories, when no global symmetries are present, is fairly well understood and classified. In recent years, attempts to generalize the latter situation through the so called 2-gauge theories have opened the door to interesting new models and new topological phases, not described by the previous schemes of classifica- tion. In this paper we go even beyond the 2-gauge construction by considering a class of models that live in arbitrary higher dimensions. These models are embedded in a structure of chain complexes of abelian groups, forcing to generalize the usual notion of gauge configurations. The advantage of such an approach is that, the topological order is explicitly manifest when the ground state space of these models is described. This is done in terms of a cohomology with coefficients in a finite chain complex. Furthermore, we show that the ground state degeneracy underpins a convenient set of quantum num- bers that label the states and that have been completely characterized. We also show that abelian examples of 1-gauge 2-gauge theories are recovered as special cases of this construction.

No description available.

No description available.