Cette thèse est consacrée à l'étude mathématique et numérique du modèle de Hartree-Fock-Bogoliubov (HFB) pour les systèmes quantiques attractifs, qui est abondamment utilisé en physique nucléaire. Après avoir présenté le modèle et ses principales caractéristiques, nous expliquons comment le discrétiser et nous montrons des résultats de convergence. Nous examinons tout particulièrement l'algorithme de point fixe (parfois appelé Roothaan) et montrons qu'il converge ou alors oscille entre deux états dont aucun n'est solution du problème. Ceci généralise au cadre HFB des résultats de Cancès et Le Bris pour le modèle plus simple de Hartree-Fock dans le cas répulsif. Suivant ces mêmes auteurs, nous proposons un algorithme basé sur la contrainte relachée et pour lequel la convergence est garantie. Dans dernière partie de la thèse, nous illustrons le comportement de ces algorithmes par des simulations numériques pour plusieurs modèles. Dans un premier temps nous considérons un système purement gravitationnel où les particules interagissent avec le potentiel de Newton. Nos simulations montrent que la matrice d'appariement est toujours non nulle, un fait qui n'a pas encore pu être démontré rigoureusement. Nous étudions ensuite un modèle très simplifié pour la description de protons et neutrons dans le noyau atomique.

The main contribution of this thesis concerns the application of the Luttinger-Ward formalism to the study of the thermodynamical properties of nuclear matter. This formalism is devoted to compute the different thermodynamical potentials from the Green's functions and therefore offers a consistent theoretical framework within which the microscopic as well as the macroscopic properties of nuclear matter can be treated at the same level.In this thesis, the Luttinger-Ward formalism has been applied to nuclear matter within two different approximations. The Hartree-Fock approximation leads to unrealistic results, but it is very useful to check the validity of the formalism in the mean-field case. Within the ladder approximation, the application of the Luttinger-Ward formalism leads to analytical results for the thermodynamical potentials in terms of the microscopical properties of the system. Therefore, using the Self-Consistent Green's Function scheme, which offers a realistic description of nuclear systems at the microscopical level, one obtains a set of microscopical properties (spectral functions, NN interaction in the medium, etc) which can be used directly in the calculation of the thermodynamical observables of dense matter.In particular, in this thesis special attention has been paid to the computation of the entropy of a system of correlated nucleons within the dynamical quasi-particle approximation. From this quantity, the free energy as well as other thermodynamical potentials of the system have been computed, leading to a full characterization of nuclear matter at the macroscopic level. In addition, the thermodynamical consistency of the approach has been shown by means of the microscopic and macroscopic chemical potentials. Finally, the liquid-gas phase transition of nuclear matter has been studied at a qualitative level. / La principal contribució d'aquesta tesi ha estat l'aplicació del formalisme de Luttinger-Ward a l'estudi de les propietats termodinàmiques de la matèria nuclear. Aquest formalisme permet obtenir els diferents potencials termodinàmics a partir de les funcions de Green i constitueix doncs un marc teòric consistent en què les propietats microscòpiques i macroscòpiques de la matèria nuclear poden ser tractades al mateix nivell.En aquesta tesi, el formalisme de Luttinger-Ward s'ha aplicat a la matèria nuclear per a dues aproximacions diferents. En l'aproximació de Hartree-Fock, els resultats obtinguts són poc realistes, però permeten comprovar la validesa del formalisme en el cas del camp mig. En l'aproximació d'escala, l'aplicació del funcional de Luttinger-Ward dóna resultats analítics per als potencials termodinàmics a partir de les propietats microscòpiques del sistema. D'aquesta manera, mitjançant l'esquema de Funcions de Green Autoconsistents, que ofereix una descripció realista del sistema nuclear a nivell microscòpic, obtenim una sèrie de propietats microscòpiques (funcions espectrals, interacció NN en el medi nuclear, etc) que poden ser utilitzades directament en el càlcul dels observables termodinàmics de la matèria densa.En particular, en aquesta tesi hem fet èmfasi en el càlcul de l'entropia d'un sistema de nucleons correlacionats en l'aproximació de quasi-partícula dinàmica. A partir d'aquesta quantitat, s'han obtingut l'energia lliure i altres potencials termodinàmics del sistema, fet que ens permet caracteritzar-lo a nivell macroscòpic. A més, s'ha demostrat la consistència termodinàmica de l'aproximació a partir de càlculs del potencial químic macroscòpic i microscòpic. Finalment, s'ha estudiat de manera qualitativa la transició líquid-gas de la matèria nuclear. / RESUMEN:La principal contribución de esta tesis concierne la aplicación del formalismo de Luttinger-Ward al estudio de las propiedades termodinámicas de la materia nuclear. Este formalismo permite obtener los diferentes potenciales termodinámicos a partir de las funciones de Green y constituye por lo tanto un marco teórico consistente en el que las propiedades microscópicas y macroscópicas de la materia nuclear pueden ser tratadas al mismo nivel.En esta tesis, el formalismo de Luttinger-Ward se ha aplicado a la materia nuclear para dos aproximaciones distintas. En la aproximación de Hartree-Fock, los resultados obtenidos son poco realistas, pero permiten comprobar la validez del formalismo en el caso del campo medio. En la aproximación de escalera, la aplicación del funcional de Luttinger-Ward da lugar a resultados analíticos para los potenciales termodinámicos a partir de las propiedades microscópicas del sistema. De este modo, mediante el esquema de Funciones de Green Autoconsistentes, que ofrece a una descripción realista del sistema nuclear a nivel microscópico, obtenemos una serie de propiedades microscópicas (funciones espectrales, interacción NN en el medio nuclear, etc) que pueden ser usadas directamente en el cálculo de los observables termodinámicos de la materia densa.En particular, en esta tesis se ha prestado especial atención al cálculo de la entropía de un sistema de nucleones correlacionados en la aproximación de quasi-partícula dinámica. A partir de esta cantidad, se ha obtenido la energía libre, así como otros potenciales termodinámicos del sistema, lo que nos permite caracterizarlo a nivel macroscópico. Así mismo, se ha demostrado la consistencia termodinámica de la aproximación a partir de los cálculos del potencial químico macroscópico y microscópico. Finalmente, se ha estudiado de forma cualitativa la transición líquido-gas de la materia nuclear.

In this work, the doping processes of the SA type stepped Ge (100) surface by arsine (AsH3) and diborane (B2H6) gas flow have been simulated seperately by the possible adsorption and dissociation models. The most stable adsorption and dissociation models of AsH3 and B2H6 on stepped Ge(100) surface have been determined by the local minimum total energy and/or binding energy calculations based on Hartree-Fock Theory. The present calculations have shown that, the step region (both up and down terraces) of the stepped Ge (100) surface has the most attractive sites for the initial adsorption stages of the gas molecules. It has been found that the thermodynamically preferred structures in the dissociation paths of arsine and diborane are the same / AsH3 , BH3 (fragment of diborane), AsH2 and BH2 products prefer to be bounded to a single surface Ge atom, but AsH and BH prefer to be bridged between two adjacent surface Ge atoms. It has been also found that, at the first step of the adsorptions, AsH3 can only dissociate to AsH2, but BH3 can dissociate to both BH2 and BH. This remarkable result has showed that dissociation of BH3 on Ge(100) surface can be easier than AsH3&rsquo / s. According to the optimization calculations, the dissociation path has started with the adsorption of AsH3 (or BH3) on the electron deficient side (buckled down) of the Ge dimer bond and ended with the occupation of the empty Ge sites in the surface layers by As (or B) atom substitutionally. In the present work, the beginning of the n &ndash / (or p-) type doping of the stepped Ge(100) surface has been illustrated by the As (or B) electronic states obtained in the optical energy gap of Ge very close to HOMO (or LUMO) energy edge.

<p>The X-ray absorption spectrum of silicon in of SiCl4 has been calculated for the LIII and LII edges. The resulting spectrum has been vibrationally resolved by considering the symmetric stretch vibrational mode and the results has been compared to experiment [4]. One peak from the experiment was found to be missing in the calculated vibrationally resolved spectrum. The other calculated peaks could be matched to the corresponding experimental peaks although significant basis set effects are present. An investigation of one peak beyond the Franck–Condon principle shows it to be a good approximation in the case of the studied system.</p>

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 161-175). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 161-175). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 86-90).

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

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

Thesis (Ph. D. in Physics)--Vanderbilt University, Dec. 2005. / Title from title screen. Includes bibliographical references.