Thesis (Ph. D.)--University of Wisconsin--Madison, 1960. / Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 62-65).

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If there is a general theme to this thesis, it is the effects of strong correlations in both bosons and fermions. The bosonic system considered here consists of ultracold alkali atoms trapped by interfering lasers, so called optical lattices. Strong interactions, realized by increasing the depth of the lattice potential, or through the phenomenon of Feshbach resonances induce strong correlations amongst the atoms, rendering attempts to describe the systems in terms of single particle type physics unsuccessful. Of course strong correlations are not the exclusive domain of bosons, and also are not caused only by strong interactions. Other factors such as reduced dimensionality, in one-dimensional electron gases, or strong magnetic fields, in two-dimensional electron gases are known to induce strong correlations. In this thesis, we explore the manifestations of strong correlations in ultracold atoms in optical lattices and interacting electron gases. Optical lattices provide a near-perfect realization of lattice models, such as the bosonic Hubbard model (BHM) that have been formulated to study solid state systems. This follows from the absence of defects or impurities that usually plague real solid state systems. Another novel feature of optical lattices is the unprecedented control experimenters have in tuning the different lattice parameters, such as the lattice spacing and the intensity of the lasers. This control enables one to study the model Hamiltonians over a wide range of variables, such as the interaction strength between the atoms, thereby opening the door towards the observation of diverse and interesting phenomena. The BHM, and also its variants, predict various quantum phases, such as the strongly correlated Mott insulator (MI) phase that appears as a function of the parameter t/U, the ratio of the nearest neighbor hopping amplitude to the on-site interaction, which one varies experimentally over a wide range of values simply by switching the intensity of the lasers. But as always, even in these designer-made "solid state" systems, practical considerations introduce complications that blur the theoretical interpretation of experimental results, such as inhomogeneities in the lattice structure. The first part of this thesis presents a quantum theory of ultracold bosonic atoms in optical lattices capable of describing the properties of the various phases and the transitions between them. Its usefulness, compared to other approaches, we believe rests in its broad applicability and in the relative ease it handles the complications while producing quantitatively accurate results. / text

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--University of California, Berkeley, 1962. / "UC-34 Physics" -t.p. "TID-4500 (17th Ed.)" -t.p. Includes bibliographical references (p. 57-59).

It is widely believed that Quantum Chromodynamics (QCD) is the theory that describes the strong interaction. In the infrared region of the theory, the perturbative expansion breaks down and so, other techniques must be used. One such technique is the study of the Schwinger-Dyson equations. In this thesis is presented such a study. It is shown that the ghost sector of QCD may be crucial to the understanding of the infrared behaviour. Conventionally, the Slavnov- Taylor identity is used to truncate the Schwinger-Dyson equations but it is found that for the ghost-gluon vertex, such an identity cannot be used in an appropriate manner. In order to extract information, a new technique is presented, based on the powerlaw behaviour of the two-point functions in the infrared. By demanding consistency in the full equations in Landau gauge and multiplicative renormalisability, it is found that in general, the gluon propagator dressing function cannot diverge and the ghost propagator function cannot vanish in the infrared. Further, it is shown that the powerlaw behaviour depends on a certain kinematical limit of only one function connected with the ghost-gluon vertex.

Cette thèse comprend une analyse d'un système de N bosons de masse m, à une dimension (1D). Vue des efforts expérimentaux récents et de la perspective d'étudier plusieurs effets quantiques intéressants, nous choisissons une géométrie circulaire avec une circonférence L. Un potentiel extérieur dépendant du temps nous permet d'introduire un mécanisme qui change l'état du moment angulaire des bosons. Ce potentiel est de la forme d'une fonction delta de Dirac qui se déplace le long de l'anneau à une vitesse v et la force de ce potentiel vaut U_0. Il peut être vu comme une barrière qui met les bosons en rotation. Les interactions entre les bosons sont des interactions de contact, décrites dans le modèle de Lieb et Liniger. Puisque le potentiel extérieur ne garde pas la symétrie de translation de L'Hamiltonien du système l'équation de Schrödinger n'est pas résoluble de manière exacte en utilisant un Ansatz de Bethe. Cependant, dans les limites des bosons libres et des bosons impénétrables de Tonks et Girardeau des méthodes alternatives existent pour trouver une solution exacte. Le but de cette thèse est de résoudre l'équation de Schrödinger dans ces cas limites. La solution nous permet d'accéder aux observables intéressantes concernant les propriétés superfluides des bosons libres et du gaz de Tonks. Nous effectuons une analyse du courant des particules, de ses fluctuations et de la force de traînée. Nous trouvons un comportement superfluide en-dessous d'une vitesse critique v_c=ħπ/(mL) de la barrière. Une oscillation du courant et la force de traînée est observée pour une vitesse de la barrière v=n*v_c, avec n un entier naturel. De plus, nous étudions la nature de l'état quantique du gaz de Tonks. Dans les analyses de la distribution des impulsions, de la fonction de Wigner et des images ``temps de vol'' pour une vitesse de la barrière v=n*v_c, on trouve que l'état du système est une superposition macroscopique de deux sphères de Fermi, l'une centrée autour de l'impulsion égale à zéro et l'autre autour de l'impulsion égale à 2q, avec q=mv/ħ. Cet état est un état fortement corrélé, non-classique car la fonction de Wigner atteint des valeurs négatives. / Recent experimental activities of boson trapping on a ring geometry open the way to explore a novel topology. We focus on a tight ring trap with strong transverse confinement leading to an effectively one-dimensional motion along its circumference. We consider a strongly interacting bose gas on the ring subjected to a localized barrier potential which is suddenly set into motion. The Bose-Fermi mapping allows to obtain an exact solution for the many-body wavefunction in the impenetrable-boson (Tonks-Girardeau) limit of infinitely strong interactions between the particles with arbitrary external potential, not treatable with the Bethe Ansatz. Using the time-dependent extension to BF mapping an exact solution for the dynamical evolution of the many-body wavefunction is obtained. The exact solution allows to calculate the particle current, the particle current fluctuations and the drag force acting on the barrier. In the weak barrier limit the stirring drives the system into a state with net zero current and vanishingly small current fluctuations for velocities smaller than v_c=ħπ/(mL), with m the atomic mass and L the ring circumference. The existence of a velocity threshold for current generation indicates superfluid-like behavior of the mesoscopic Tonks-Girardeau gas, different from the non-superfluid behavior predicted for the TG gas in an infinite tube. At velocities approaching integer multiples of v_c angular momentum can be transferred to the fluid and a nonzero drag force arises. At these velocities we predict the formation of a macroscopic superposition of a rotating and a nonrotating Fermi sphere of the mapped Fermi gas. We calculate the momentum distribution, time of flight images and the Wigner function of the Bose gas, the latter allowing to identify quantum interferences in the superposition. We find that the barrier velocity should be larger than the sound velocity for a better discrimination of the two components of the superposition.

Dynamique du polyamide dans l'état solide en présence de solvants: Les polyamides sont une famille de polymères thermoplastiques semi-cristallins largement utilisés dans l'industrie automobile grâce à leur excellente stabilité thermique et propriétés mécaniques. Cependant, ces propriétés peuvent être affectées par la sorption de l'eau présente dans l'atmosphère ou de l'éthanol présent dans les biocombustibles. Les cinétiques de sorption et la sorption à l'équilibre dépendent des mécanismes d'interaction entre le solvant et le polyamide et des mécanismes de sorption et de diffusion. La diffusion et la sorption de solvants dans les polyamides sont des phénomènes complexes à cause de l'existence d'interactions spécifiques (liaisons hydrogène), d'hétérogénéités dynamiques dans la phase amorphe, de changements dans la dynamique du polymère en présence de solvants et de l'existence d'une phase cristalline. Puisque l'accessibilité de la phase amorphe peut avoir une influence sur les mécanismes de diffusion et de sorption, la diffusion et la sorption de différents solvants (eau, alcools de tailles différentes) ont été comparés dans un polyamide 100% amorphe et son homologue semi-cristallin. Nous avons confirmé que la phase amorphe d'un polymère semi-cristallin n'est pas entièrement accessible à l'eau, ce qui est en accord avec la littérature. Une deuxième partie de cette étude a été consacrée à la relation entre la diffusion de solvants et la dynamique de la phase amorphe. Premièrement, nous avons mis en évidence que les mécanismes de diffusion Fickien et non-Fickien peuvent être expliqués par la variation des coefficients de diffusion avec la concentration de solvant. Deuxièmement, l'influence de la relaxation du polymère a été évaluée par Spectroscopie Diélectrique. Une simple comparaison des échelles de temps de la diffusion et de la relaxation alpha, associée à la transition vitreuse, indique que les deux phénomènes ne sont pas directement corrélés. Cependant, la diffusion semble corrélée à la relaxation secondaire beta, qui décrit la dynamique locale des groupements amide en présence d'eau / Dynamics in the solid state in presence of solvents: Polyamides are a family of semi crystalline thermoplastic polymers widely employed in the automotive industry due to its excellent thermal stability and mechanical properties. However, polyamide can be significantly affected by the absorption of low molecular weight penetrants like water. The rate of sorption and amount of absorbed solvent depend on the mechanisms of interaction between solvent and polyamide, along with sorption and diffusion mechanisms. Diffusion and sorption of solvents in polymers can be very complex because of the existence of specific interactions (non-polar or polar), dynamic heterogeneities in the amorphous phase, modification of the polymer dynamics induced by the solvents and different crystalline phases. In polyamide/solvent systems, all of these factors have to be taken into account. A first part of this study focused on the accessibility of the amorphous phase in semicrystalline polyamides. A comparison between a 100% amorphous polyamide and its semicrystalline counterpart of equivalent chemical structure suggests that the amorphous phase in semi-crystalline polyamide is not entirely accessible to the solvents. A second part of this study focused on the diffusion mechanisms of water and ethanol in polyamide. Fickian or non- Fickian diffusion mechanisms could be explained by the variation of the diffusion coefficients as a function of solvent concentration. Moreover, the relationship between water diffusion and the dynamics of the amorphous phase in polyamide was investigated. A simple comparison of dielectric characteristic relaxation times with the timescale of diffusion suggests that diffusion and polyamide alpha relaxation (associated to the glass transition) should not be directly correlated. However, diffusion is correlated to the secondary beta relaxation, which encompasses the local chain dynamics of hydrogen bonded amide groups in the presence of water. A mechanism of diffusion based on the trapping of water molecules between neighboring sorption sites (amide groups) is proposed in these strongly interacting polymers

This thesis familiarizes the reader with the process behind the construction of ππ scattering amplitudes. Several representations and transformations nec- essary to pass from one to another are introduced. Then known solutions of Roy equations are employed to extract values of subthreshold parameters αππ and βππ from recent experimental data. As a second goal three-flavour chiral perturbation theory(χPT), which is a low energy effective field theory of quan- tum chromodynamics, is used to obtain theoretical predictions for αππ and βππ by applying a technique called resummed approach. A large statistical ensemble of predictions is numerically generated. Subsequently, Bayesian statistics is uti- lized to get more information about spontaneous symmetry breaking parameters X(3), Y (3), Z(3), which are related to the leading order low energy coupling constants of three-flavour χPT. These results are then compared to several other recent determinations. Significant shifts in probability distributions compared to Descotes-Genon et al. [2004] are observed. The new results are more consistent with theoretical expectations. 1 Bibliography S. Descotes-Genon, N. H. Fuchs, L. Girlanda, and J. Stern. Resumming qcd vac- uum fluctuations in three-flavor chiral perturbation theory. The European Phys- ical Journal C,...

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