<p>Time-dependent density functional theory calculations have been carried out to determine the complex first-order hyperpolarizability in the two-photon resonance region of the molecule IDS-Cab. Calculations show that three strongly absorbing states, in the ultraviolet region, are separated to the extent that no significant interference of the imaginary parts of the tensor elements of the first-order hyper-polarizability occurs. Consequently, and in contrast to experimental findings [27], no reduced imaginary parts of the first-order hyperpolarizability in the two-photon resonant region can be seen.</p>

L'interaction effective entre les nucléons est un ingrédient essentiel des<br />calculs microscopiques de structure nucléaire. L'une des formes utilisée<br />depuis les années 1970 est la force effective phénoménologique proposée par<br />D. Gogny. Cette force donne d'excellents résultats dans les noyaux à<br />l'approximation du champ moyen. La présence de composantes de contact ne<br />permet pas cependant de l'employer en toute généralité pour décrire les<br />corrélations au-delà du champ moyen qui se manifestent fréquemment dans les <br />noyaux.<br /><br />Dans ce travail, nous étudions des extensions de la force de Gogny, notamment<br />une généralisation où le terme dépendant de la densité de portée nulle est<br />remplacé par un terme de portée finie. Les paramètres intervenant dans la forme<br />analytique de la force sont ajustés sur les propriétés de la matière nucléaire<br />infinie symétrique et de la matière neutronique, et sur les observables globales<br />de quelques noyaux stables, en particulier celles associées aux corrélations<br />d'appariement. Nous présentons la méthode permettant d'inclure ce type de<br />force dans les codes de calcul Hartree-Fock-Bogoliubov et nous analysons les<br />résultats obtenus dans de nombreux noyaux. Les nouvelles versions de la force<br />de Gogny apparaissent reproduire la structure nucléaire avec une qualité égale<br />ou supérieure à la version traditionnelle.

In this thesis we employ various mean-field approaches to study the shortrange interaction effects in topological insulators. We start with the Kane-Mele model on the decorated honeycomb lattice and study the stability of topological insulator phase against different perturbations. We establish an adiabatic connection between a noninteracting topological insulator and a strongly interacting spin liquid in its Majorana fermion representation. We use the Hartree-Fock mean-field approach, slave-rotor approach and slave-boson approach to study correlation effects related to topological insulators. With the spontaneous symmetry breaking mechanism, we can have an interaction driven topological insulator with extended Hubbard models on the kagome lattice and decorated honeycomb lattice. For the interplay among spin-orbit coupling, distortion and correlation effect in transition metal oxides, we use the slave-rotor mean-field approach to study its phase transition. We identify regimes where a strong topological Mott insulator and a weak topological insulator reside due to the strong Coulomb interaction and distortion. This is relevant to experiments with the transition metal oxides as they hold promise to realize topological insulators. To study the doping effects and a possible spin liquid in Kane-Mele-Hubbard model on the honeycomb lattice, we employ the slave-boson mean-field approach which is appropriate for the intermediate interaction strength. We compare our results with those obtained from other methods. / text

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Dans cette thèse nous allons présenter nos résultats sur les différentes solutions pour le gaz d'électrons dans une bicouche de graphène sous fort champ magnétique en fonction de la différence de potentiel entre les deux couches et du facteur de remplissage entier de v = -3 à v = 3. Nos résultats seront comparés aux résultats expérimentaux pour expliquer, entre autres, l'apparition de sous plateau dans la conductivité pour les états de N = O. Nos états fondamentaux furent calculés à partir de l'approximation Hartree-Fock pour prendre en compte l'interaction coulombienne. Nous avons obtenu différentes solutions que l'on peut classifier comme les phases cohérentes : inter-couche simple, inter-couche double, inter-spin simple, inter-spin double et orbitale. Le reste des solutions que nous avons trouvées sont des phases sans cohérence. Ces phases peuvent être décrites comme des ferro-aimants de pseudo-spin de Hall. Pour chacune de ces phases, nous avons calculé les modes collectifs et l'absorption électromagnétique à l'aide de la théorie "Generalized Random-Phase Approximation" (GRPA) et le gap d'excitation du système. Nous avons porté une attention particulière aux modes collectifs dans la phase orbitale qui montrent une instabilité et à montrer que cette instabilité peut être décrite par une interaction de type Dzyaloshinskii-Moriya (DM) dans un hamiltonien effectif de spin pour décrire les modes collectifs. Nous avons aussi calculé des effets magnéto-électriques en calculant le changement de polarisation de spin qui se produit en appliquant un champ électrique dans le plan des couches aux facteurs de remplissage v = ±1, ±2.

Ce travail porte sur l'étude d'isotopes de cesium (118,146Cs) et de francium (207-213Fr et 220-228Fr) par spectroscopie atomique hyperfine et sur l'interprétation de ces résultats du point de vue nucléaire. Les grandeurs nucléaires mesurées sont : le spin, le moment magnétique, le moment quadrupolaire électrique et le rayon carré moyen de charge. La technique employée, basée sur le pompage optique hyperfin à l'aide d'un laser accordable, puis la sélection magnétique des atomes est décrite dans la première partie. Les résultats de ces mesures atomiques y sont également présentés. Dans la seconde partie, ces résultats sont interprétés dans le cadre de modèles nucléaires. Les déformations des isomères des césiums légers sont comparées aux valeurs obtenues par un calcul théorique auto-consistant. Les isotopes de francium lourds se trouvent dans une région où est prédite l'existence de déformations octupolaires statiques. L'effet pair-impair mesuré sur le rayon carré moyen est anormal dans cette région. Mais les résultats expérimentaux ne permettent pas de conclure définitivement quant à la nature de ces déformations.

Made available in DSpace on 2014-06-12T23:15:24Z (GMT). No. of bitstreams: 2 arquivo922_1.pdf: 2140122 bytes, checksum: 2395f0c169638407a7012a715b3f3688 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O desenvolvimento e implementação de métodos de dinâmica direta, como dinâmica molecular de Born-Oppenheimer (BOMD) e de Car-Parrinello (CPMD), estão facilitando os estudos das dinâmicas de reações químicas e mostrado as limitações das teorias estatísticas (estado de transição e coordenada de reação intrínseca), além de permitir a descoberta de novos mecanismos de reações químicas. Entretanto, estes métodos ainda apresentam limitações, como por exemplo, tratamento clássico dos núcleos e não inclusão dos acoplamentos entre os movimentos dos elétrons e dos núcleos. O formalismo da dinâmica de elétrons-núcleos (END) permite a correção dessas duas falhas, além de outras, e pode ser vista como o próximo passo a ser dado no aprimoramento das descrições das dinâmicas de reações químicas. O formalismo END é apresentado e os detalhes da implementação da sua aproximação mais básica (END-1) no programa ENDyne são discutidos. Nela, as equações de movimento envolvem acoplamentos entre os movimentos dos elétrons e dos núcleos, formando um sistema de equações não lineares. Dinâmicas realizadas nessas condições acabam por acessar estados excitados, fazendo com que os conjuntos de funções de base disponíveis não sejam os mais adequados, pois, geralmente, são obtidos para descrever o estado fundamental. Sendo assim, novos conjuntos de funções de base foram desenvolvidos para os elementos da primeira fila da tabela periódica, em que os estados excitados também foram considerados na elaboração e otimização destes conjuntos. De fato, a aplicação destes novos conjuntos de funções de base em cálculos de energias de excitação de moléculas e de seções de choque de transferência de elétron em colisões próton-átomo, com o método END-1, demonstrou a importância e a relevância desses conjuntos. O método END-1 foi também utilizado no estudo das dinâmicas das colisões de íons altamente carregados (N6+ e O7+) com metano, culminando na determinação das seções de choque e das probabilidades de transferência de 1, 2, 3 e mais de 3 elétrons. Estes resultados corroboram os valores experimentais e fornecem explicações detalhadas das diferenças qualitativas e quantitativas observadas entre estes íons. Ainda, análises preliminares da explosão Coulombiana a ser sofrida pelo alvo (CH4) são iniciadas. As colisões de hidrogênio com os sistemas mono-eletrônico efetivos Si3+, C3+ e O3+ também foram estudadas com o método END-1 e forneceram resultados quantitativos para as seções de choque de transferência de carga equivalente aos experimentais, demonstrando a eficiência da teoria END mesmo para sua aproximação mais básica Por fim, a teoria do formalismo END para função de onda eletrônica multideterminantal, denominada de vector Hartree-Fock (VHF), é apresentada, assim como alguns conceitos referentes ao código do programa ENDyne

Le modèle du jellium est l'un des modèles fondamentaux de la matière condensée.Il est constitué d'un ensemble d'électrons et d'un fond uniforme qui assure la neutralité globale.À température nulle et sans champ extérieur, la densité électronique est le seul paramètre du système.Malgré la simplicité de ce modèle, l'état fondamental du jellium en fonction de la densité reste un problème ouvert.Nous avons étudié le modèle du jellium à 2 et 3 dimensions dans l'approximation de Hartree-Fock par une méthode numérique de descente.En utilisant des états périodiques, le nombre d’inconnues est grandement réduit et le nombre d’électrons peut atteindre le million.À type de réseau et polarisation fixés, nous montrons que le système forme un cristal de Wigner à basse densité puis, au dessus d'une densité de transition, occupe des états «métalliques» caractérisés par une structure cristalline avec une maille plus petite que celle du cristal de Wigner.Les états métalliques interpolent entre le cristal de Wigner et le gaz de Fermi, ce dernier n'étant retrouvé qu'à densité infinie.Ce comportement se retrouve à deux et trois dimensions, pour un gaz polarisé et non polarisé, et pour les différents type de réseaux considérés dans nos travaux.Le diagramme de phase à deux ou trois dimensions est alors très riche et comprend à basse densité diverses phases «cristal de Wigner» avec des symétries et polarisations différentes.À haute densité, les états métalliques non-polarisées déstabilisent le cristal de Wigner et le gaz de Fermi. Ces états métalliques s’interprètent comme une superposition d’ondes de densité de spin, prédite par Overhauser en 1962. / The jellium model is a fundamental model in condensed matter. It is formed by a set of electrons and a uniform background insuring global neutrality. At zero temperature and without external field, the ground-state depends only on the electronic density. Despite its simplicity, the jellium ground-state is still an open problem. We studied the jellium model in 2 and 3 dimensions within the Hartree-Fock approximation using a numerical descent method. Assuming periodic states, we greatly reduce the number of unknowns and the system may contain up to one million of electrons. At fixed lattice symmetry and polarization, the ground-state is a Wigner crystal at low density, and a «metallic state» above a critical density value. These metallic states are crystals with a lattice constant smaller than in Wigner phase, and interpolate between the latter and the Fermi gas. The metallic states exists in two and three dimensions, for a polarized and unpolarized gas, and for various lattice symmetries. Therefore, the jellium phase diagram at zero temperature is rich : it contains several Wigner crystal phases at low density, polarized and unpolarized, and an unpolarized metallic state at high density. These states are well described by a superposition of spin-density waves, as predicted by Overhauser in 1962.

This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n). A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method. / <p>QC 20101123</p>

Phonon anharmonicity is critical for describing various phenomena in crystals, including lattice thermal conductivity, thermal expansion, structural phase transitions, and many others. Including anharmonicity in the calculation of condensed matter observables developed rapidly in the past decade. First-principles computation of cubic phonon interactions have been performed in many systems, and the quartic interactions have begun to receive more attention. In this study, reliable Hamiltonians are constructed purely in terms of quadratic, cubic, and quartic irreducible derivatives, which are calculated efficiently and precisely using the lone and bundled irreducible derivative approaches (LID and BID). The resulting Hamiltonians give rise to a nontrivial many-phonon problem which requires some approximation in order to compute observables. We implemented self-consistent diagrammatic approaches to evaluate the phonon self-energy, including the Hartree-Fock approximation for phonons and quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Additionally, we implemented molecular dynamics in order to yield the numerically exact solution in the classical limit. The molecular dynamics solution is robust for directly comparing to experimental results at sufficiently high temperatures, and for assessing our diagrammatic approaches in the classical limit. Anharmonic vibrational Hamiltonians were constructed for CaF₂, ThO₂, and UO₂. Diagrammatic approaches were used to evaluate the phonon self-energy, yielding the phonon lineshifts and linewidths and the thermal conductivity within the relaxation time approximation. Our systematic results allowed us to resolve the paradox of why first-principles phonon linewidths strongly disagree with results extracted from inelastic neutron scattering (INS). We demonstrated that the finite region in reciprocal space required in INS data analysis, the 𝑞-voxel, must be explicitly accounted for within the calculation in order to draw a meaningful comparison. We also demonstrated that the 𝑞-voxel is important to properly compare the spectrum measured in inelastic X-ray scattering (IXS), despite the fact that the ?-voxel is much smaller. Accounting for the 𝑞-voxel, we obtained good agreement for the scattering function linewidths up to intermediate temperatures. Additionally, good agreement was obtained for the thermal conductivity. Another topic we addressed is translation symmetry breaking caused by factors such as defects, chemical disorders, and magnetic order. These phenomena will lead to shifts and a broadening of the phonon spectrum, and formally the single-particle Green’s function encodes these effects. However, it is often desirable to obtain an approximate non-interacting spectrum that contains the effective shifts of the phonon frequencies, allowing straightforward comparison with experimentally measured scattering peak locations. Such an effective phonon dispersion can be obtained using a band unfolding technique, and in this study, we formulated unfolding in the context of irreducible derivatives. We showcased the unfolding of phonons in UZr₂, where chemical disorder is present, and compared the results with experimental IXS data. Additionally, we extended the unfolding technique to anharmonic terms and demonstrated this using 3rd and 4th order terms in the antiferromagnetic phase of UO₂.