Made available in DSpace on 2016-04-28T14:16:26Z (GMT). No. of bitstreams: 1 CarlosNegretti.pdf: 1213179 bytes, checksum: b4db34b2eaca3e036fb14e0b7dc37436 (MD5) Previous issue date: 2006-06-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Russian biochemist Alexandre Ivanovicth Oparin , in 1924 in the former Soviet Union wrote an article in which he puts forward his hypothesis about a delicate subject in the history of biology: the origin of life on Earth. Proposes his hypothesis about th origin of life relating the biological evolution mainly the Natural Selection Theory of Charles Darwin with the Dialectic Materialism of Karl Marx and Friedrich Engels. There are some disagreements about the nature of such relation, which is considered by some authors coherent and by others just adequate to political pressures of the Stanilist regime in the former Soviet Union. From a comparative analysis between the books of Engels mainly Dialectic of Nature, in with his conception of nature and dialectic materialism are present and Oparin s articles, this work shows that such concepts helped Oparin to develop his lage hypothesis with a sophistication in terms of argument, to the philosophical point of view as well as experimental / O bioquímico russo Alexandre Ivanovicth Oparin publica, em 1924, na antiga União Soviética, um artigo contendo sua hipótese acerca de um ponto considerado nevrálgico da história da biologia: o problema da origem da vida na Terra. Oparin propõe sua hipótese sobre a origem da vida relacionando o evolucionismo biológico, principalmente a teoria da seleção natural de Charles Darwin, com o materialismo dialético de Karl Marx e Friedrich Engels. Há divergências quanto à natureza de tal relação, considerada, por alguns autores, coerente e, por outros, forçada por pressões políticas presentes no contexto em que Oparin viveu, sob o regime stalinista da antiga União Soviética. A partir de uma análise comparativa entre os livros de Engels principalmente Dialética da natureza, no qual sua concepção de natureza e do materialismo dialético são presentes e publicações de Oparin, este trabalho mostra que tais concepções serviram a este último para o desenvolvimento posterior de sua hipótese, como uma certa sofisticação em termos de argumentos, tanto do ponto de vista filosófico como experimental

Les systèmes de spin antiferromagnétiques en une dimension présentent des caractéristiques remarquables. Le théorème de Mermin-Wagner montre que même dans l'état fondamental de leur Hamiltonien, ces systèmes ne possèdent pas d'ordre à longue distance dans leurs fonctions de corrélation spin-spin s'ils possèdent une symétrie continue. Néanmoins, un quasi-ordre à longue distance peut exister, avec des fonctions de corrélation spin-spin décroissant en loi de puissance avec la distance, comme par exemple dans la chaîne de spin-1/2. Ce cas est décrit par la théorie des liquides de Luttinger. Même dans le cas d'un ordre à courte distance où les fonctions de corrélations spin-spin décroissent exponentiellement, un ordre topologique peut être présent. Il peut être mis en évidence par un paramètre d'ordre dépendant des opérateurs de spin de façon non-locale ou par la présence d'excitations de bord, comme par exemple dans le cas de la chaînes de spin-1. D'autre part, il existe une équivalence formelle entre les opérateurs de spin-1/2 et les bosons de coeur dur, qui permet de traduire les propriétés des systèmes magnétiques dans le langage des bosons en interaction. Après une rapide revue des méthodes théoriques utilisées pour la description des systèmes de basse dimensionnalité, je décrirais mes travaux sur les systèmes échelles de spin antiferromagnétiques et les applications aux systèmes de bosons en interaction.

This thesis covers most of my work in the field of ultracold atoms loaded in optical lattices. This thesis can be divided into five different parts. In Chapter 1, after a brief introduction to the field of optical lattices I review the fundamental aspects pertaining to the physics of systems in periodic potentials and a short overview of the experiments on ultracold atoms in an optical lattice. In Chapter 2 we develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this poten¬tial, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator(MI), density-wave(DW), and supersolid (SS) phases in the plane of the chemical potential and on-site repulsion ; we present phase diagrams for representative values of , the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI ,DW ,and SSphases. We explore the implications of our study for experiments on cold-atom dipolar con¬densates in optical lattices in a confining potential. In Chapter3 we present an extensive study of Mottinsulator( MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with har¬monic traps. For this we develop an inhomogeneous mean-field theory. Our results for the BH model with one type of spinless bosons agrees quantitatively with quan¬tum Monte Carlo(QMC) simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional(3D) systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also generalize our inhomogeneous mean-field theory to study BH models with har¬monic traps and(a) two species of bosons or(b) spin-1bosons. With two species of bosons we obtain rich phase diagrams with a variety of SF and MI phases and as¬sociated shells, when we include a quadratic confining potential. For the spin-1BH model we show, in a representative case, that the system can display alternating shells of polar SF and MI phases; and we make interesting predictions for experi¬ments in such systems. . In Chapter 4 we carry out an extensive study of the phase diagrams of the ex-tended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane ¬insulator(HI) phases. We show that the critical exponents and central charge for the HI-DW,MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) uni¬versality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different bound¬ary conditions lead to different phase diagrams.. In Chapter 5 we obtain the excitation spectra of the following three generalized of Bose-Hubbard(BH) models:(1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH) for spinless interacting bosons of one species. In all the phases of these models we show how to obtain excitation spectra by using the random phase approximation (RPA). We compare the results of our work with earlier studies of related models and discuss implications for experiments.