Cette thèse est consacrée à l'étude du modèle de Hubbard unidimensionnel et à ses généralisa- tions. Le modèle de Hubbard est un modèle fondamental de la physique de la matière condensée, décrivant des électrons en interaction sur un réseau. Il a une très riche structure physique. Malgré la simplicité de sa construction, le modèle a été appliqué dans différents problèmes comme la supra- conductivité à haute température, le magnétisme et la transition métal-isolant. A une dimension, le modèle de Hubbard est un modèle intégrable très étudié qui a servi de 'laboratoire' pour la physique de la matière condensée. Récemment, les systèmes intégrables quantiques d'une facon générale, et le modèle de Hubbard en particulier, sont apparus d'une manière surprenante dans le contexte de la correspondance AdS/CFT. Le point de contact entre ces domaines est les équations de Bethe : celles de nouveaux modèles intégrables et de modèles existants généralisés sont à priori significatifs dans l'application en dualité AdS/CFT. Dans la premiere partie de la thèse, les notions de base sur l'intégrabilité quantique sont présen- tées : formalisme de la matrice R, équation de Yang-Baxter, chaînes de spin intégrables. Dans la deuxième partie, certaines résultats fondamentaux concernant le modèle de Hubbard sont passés en revue : la solution par l'Ansatz de Bethe coordonnée, les solutions réelles des équations de Lieb-Wu etc. De plus, l'application dans la correspondance AdS/CFT est considérée. Cependant, on trouve que certaines modifications du modèle de Hubbard sont nécessaires pour reproduire les résultats de cette correspondance. Cela est une des motivations principales d'étude de modèles de Hubbard généralisés. La quatrième partie est consacrée aux généralisations du modèle de Hubbard, en se con- centrant sur les cas supersymétriques. La chapitre cinq expose les résultats obtenus dans le cadre de cette thèse sur les modèles de Hubbard généralisés, en particulier, l'Ansatz de Bethe coordonnée ainsi que les solutions réelles des équations de Bethe obtenues dans la limite thermodynamique. Les équations de Bethe obtenues sont différentes de celle de Lieb et Wu par des phases dont la manifesta- tion est un signe encourageant pour l'application en AdS/CFT contexte. Les applications possibles, notamment dans le domaine de la physique de la matière condensée, sont également considérées.

No description available.

We first study noninteracting electrons moving on corner-sharing tetrahedral lattices, which represent the conduction path of LiAlyTi2−yO4. A uniform box distribution type of disorder for the on-site energies is assumed. Using the Dyson-Mehta Delta-3 statistics as a criterion for localization, we have determined the critical disorder (Wc/t = 14.5 ± 0.25) and the mobility-edge trajectories. Then we study the Anderson-Hubbard model, which includes both interactions and disorder, using a real-space self-consistent Hartree-Fock theory. We provide a partial assessment on how the Hartree-Fock theory approximates the ground states of the Anderson-Hubbard model, using small clusters which can be solved exactly. The Hartree-Fock theory works very well in reproducing the ground-state energies and local charge densities. However, it does not work as well in representing the spin-spin correlations. To find the ground state, one needs to allow maximum degree of freedom in spins. Evidence of screening of disorder by the interactions is provided. We have applied the Hartree-Fock theory to large-scale three-dimensional simple cubic lattices. For a disorder strength of W/t = 6, weak interactions (U/t ≤ 3) enhance the density of states at the Fermi level and the low-frequency conductivity. There are no local magnetic moments, and the AC conductivity is Drude-like. With stronger interactions (U/t ≥ 4), the density of states at the Fermi level and the low-frequency conductivity are both suppressed. These are accompanied by the presence of local magnetic moments, and the conductivity becomes non-Drude-like. A metal-to-insulator transition is likely to take place at a critical Uc/t ≈ 8 – 9. We find that (i) the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition; (ii) the form of magnetic moments does not matter; and (iii) these results do not depend on the type of lattice or the type of disorder. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-05-26 02:20:04.652

This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function approach. We then study Anderson localization of electrons from the response of the Anderson-Hubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet di erent from weakly correlated ones. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-31 09:51:47.155

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This project presents regional velocity measurements for the eastern portion of the St. Elias Mountains, including the entire glaciated area of Kluane National Park, derived from speckle tracking of Radarsat-2 imagery acquired in winter 2011 and 2012. This technique uses a cross-correlation approach to determine the displacement of the ‘speckle’ pattern of radar phase returns between two repeat-pass images. Further reconstruction of past velocities is performed on a selection of key glaciers using feature tracking of Landsat-5 imagery, allowing for the investigation of variability in glacier motion on interannual and decadal time scales. The results of the analysis showed that there is a strong velocity gradient across the region reflecting high accumulation rates on the Pacific-facing slope of the mountain range. These glaciers may have velocities an order of magnitude greater than glaciers of a similar size on the landward slope. Interannual variability was high, both in relation to surge events, of which a number were identified, and variation of other unknown controls on glacier motion. A long-term trend of velocity decrease was observed on the Kaskawulsh Glacier when comparing the results of this analysis to work carried out in the 1960s, the pattern of which is broadly congruent to measurements of surface elevation change over a similar period.

This Ph.D. thesis in mathematical physics concerns systems of interacting fermions with strong correlations. For these systems the physical properties can only be described in terms of the collective behavior of the fermions. Moreover, they are often characterized by a close competition between fermion localization versus delocalization, which can result in complex and exotic physical phenomena. Strongly correlated fermion systems are usually modelled by many-body Hamiltonians for which the kinetic- and interaction energy have the same order of magnitude. This makes them challenging to study as the application of conventional computational methods, like mean field- or perturbation theory, often gives unreliable results. Of particular interest are Hubbard-type models, which provide minimal descriptions of strongly correlated fermions. The research of this thesis focuses on such models defined on two-dimensional square lattices. One motivation for this is the so-called high-Tc problem of the cuprate superconductors. A main hypothesis is that there exists an underlying Fermi surface with nearly flat parts, i.e. regions where the surface is straight. It is shown that a particular continuum limit of the lattice system leads to an effective model amenable to computations. This limit is partial in that it only involves fermion degrees of freedom near the flat parts. The result is an effective quantum field theory that is analyzed using constructive bosonization methods. Various exactly solvable models of interacting fermions in two spatial dimensions are also derived and studied. / QC 20111207

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

Stuttgart, Univ., Diss., 2003.

Stuttgart, Univ., Diss., 2006.