The Schrodinger Hamiltonian for a single electron in a crystalline solid with independent, identically distributed (i.i.d.) single-site potentials has been well studied. It has the form of a diagonal potential energy operator, which contains the random variables, plus a kinetic energy operator, which is deterministic. In the less-understood cases of multiple interacting charge carriers, or of correlated random variables, the Hamiltonian can take the form of a random block-diagonal operator, plus the usual kinetic energy term. Thus, it is of interest to understand the eigenvalue statistics for such operators. In this work, we establish a criterion under which certain random block operators will be guaranteed to satisfy Wegner, Minami, and higher-order estimates. This criterion is phrased in terms of properties of individual blocks of the Hamiltonian. We will then verify the input conditions of this criterion for a certain quasiparticle model with i.i.d. single-site potentials. Next, we will present a progress report on a project to verify the same input conditions for a class of one-dimensional, single-particle alloy-type models. These two results should be sufficient to demonstrate the utility of the criterion as a method of proving Wegner and Minami estimates for random block operators. / Ph. D.

O problema da universalidade do Efeito de Localização Fraca (ELF) juntamente com correções em ordem 1/N do modelo de Wegner [13] são estudadas em presença de campo magnético utilizando os auto- estados exatos de Landau segundo o método da referencia [6]. Inicialmente calculamos a magnetocondutividade de um gás de elétrons com massas anisotrópicas onde os potenciais espalhadores são distribuidos aleatoriamente. Posteriormente, focalizamos um sistema de duas bandas desordenado onde são permitidos espalhamentos intrabandas e interbandas. Este modelo é explorado com e sem campo magnético. Os resultados indicam que a universalidade do ELF nos modelos citados acima se mantém no limite de campo fraco , bastando redefinir uma constante de difusão e um tempo de relaxação efetivos. Num segundo momento, também calculamos correções em ordem 1/ N à magnetocondutividade no modelo de Wegner em três dimensões pelo método já citado, obtendo que a divergência no limite infravermerlho é eliminada pela presença do campo através da frequência de ciclotron. Um ponto importante a respeito deste modelo é a maneira como calculamos a magnetocondutividade dada a complexidade dos diagramas de Feynman que aparecem a ordem 1/ N neste modelo. Mostramos que , de maneira geral, existem duas formas equivalentes de calculo daquela quantidade (fórmula de Einstein e Abrikosov) . No entanto, pela estrutura de cada uma delas e sob certas circunstancias bem especificas, como por exemplo, os potenciais aleatórios serem. de contato, alguns diagramas que aparecem na expansão perturbativa de uma forma de cálculo (Einstein) , são suprimidos em outra (Abrikosov) , fato este que pode trazer simplificações, como é o caso concreto do modelo de Wegner em limite de campo fraco. Isto faz com que adotemos a fórmula de Abrikosov como estrategia de calculo da condutividade em todos os modelos estudados neste trabalho. / The problem of the universality of the weak localization Effect (WLE) and corrections in order 1/N to Wegner's model are studied in the presence of a magnetic field with a method based on Landau exact eigen-states according to the reference [6]. First , the magnetoconductivity of an anisotropic mass electron gas, in which the scatterer potentials are distributed randomly, was calculated. Second, it was studied a two band disordered system, in which intraband and interband scatterings are allowed. This model is explored with and without magnetic field. The results show that the WLE universality in the models mentioned before remains in the weak field limit, since an effective constant of difusion and an effective time of relaxation are redefined. After that , it were also calculated corrections in order 1/N to the magnetoconductivity in the Wegner's model in three dimensions with the method mentioned before that and the result was the divergence in the infra-red limit is eliminated by the field presence through the cyclotron frequency. Because the complexity of the Feynman diagrams in this model. it is important to highlight the way the magnetoconductivity was calculated. In general it was showed that there are two equivalent ways to calculate that quantity (Einstein and Abrikosov formulas) . Howewer, because of their structures and under certain specific circunstances, such as contact random potentials , some diagrarns which appear in the perturbative expansion of one kind of calculation (Einstein) are supressed in the other (Abrikosov) . This fact may offer some simplification, as it is the case in the Wegner model in weak field limit. For this, Abrikosov formula was used to calculate the conductivity in all the models studied in this thesis.

O problema da universalidade do Efeito de Localização Fraca (ELF) juntamente com correções em ordem 1/N do modelo de Wegner [13] são estudadas em presença de campo magnético utilizando os auto- estados exatos de Landau segundo o método da referencia [6]. Inicialmente calculamos a magnetocondutividade de um gás de elétrons com massas anisotrópicas onde os potenciais espalhadores são distribuidos aleatoriamente. Posteriormente, focalizamos um sistema de duas bandas desordenado onde são permitidos espalhamentos intrabandas e interbandas. Este modelo é explorado com e sem campo magnético. Os resultados indicam que a universalidade do ELF nos modelos citados acima se mantém no limite de campo fraco , bastando redefinir uma constante de difusão e um tempo de relaxação efetivos. Num segundo momento, também calculamos correções em ordem 1/ N à magnetocondutividade no modelo de Wegner em três dimensões pelo método já citado, obtendo que a divergência no limite infravermerlho é eliminada pela presença do campo através da frequência de ciclotron. Um ponto importante a respeito deste modelo é a maneira como calculamos a magnetocondutividade dada a complexidade dos diagramas de Feynman que aparecem a ordem 1/ N neste modelo. Mostramos que , de maneira geral, existem duas formas equivalentes de calculo daquela quantidade (fórmula de Einstein e Abrikosov) . No entanto, pela estrutura de cada uma delas e sob certas circunstancias bem especificas, como por exemplo, os potenciais aleatórios serem. de contato, alguns diagramas que aparecem na expansão perturbativa de uma forma de cálculo (Einstein) , são suprimidos em outra (Abrikosov) , fato este que pode trazer simplificações, como é o caso concreto do modelo de Wegner em limite de campo fraco. Isto faz com que adotemos a fórmula de Abrikosov como estrategia de calculo da condutividade em todos os modelos estudados neste trabalho. / The problem of the universality of the weak localization Effect (WLE) and corrections in order 1/N to Wegner's model are studied in the presence of a magnetic field with a method based on Landau exact eigen-states according to the reference [6]. First , the magnetoconductivity of an anisotropic mass electron gas, in which the scatterer potentials are distributed randomly, was calculated. Second, it was studied a two band disordered system, in which intraband and interband scatterings are allowed. This model is explored with and without magnetic field. The results show that the WLE universality in the models mentioned before remains in the weak field limit, since an effective constant of difusion and an effective time of relaxation are redefined. After that , it were also calculated corrections in order 1/N to the magnetoconductivity in the Wegner's model in three dimensions with the method mentioned before that and the result was the divergence in the infra-red limit is eliminated by the field presence through the cyclotron frequency. Because the complexity of the Feynman diagrams in this model. it is important to highlight the way the magnetoconductivity was calculated. In general it was showed that there are two equivalent ways to calculate that quantity (Einstein and Abrikosov formulas) . Howewer, because of their structures and under certain specific circunstances, such as contact random potentials , some diagrarns which appear in the perturbative expansion of one kind of calculation (Einstein) are supressed in the other (Abrikosov) . This fact may offer some simplification, as it is the case in the Wegner model in weak field limit. For this, Abrikosov formula was used to calculate the conductivity in all the models studied in this thesis.

O problema da universalidade do Efeito de Localização Fraca (ELF) juntamente com correções em ordem 1/N do modelo de Wegner [13] são estudadas em presença de campo magnético utilizando os auto- estados exatos de Landau segundo o método da referencia [6]. Inicialmente calculamos a magnetocondutividade de um gás de elétrons com massas anisotrópicas onde os potenciais espalhadores são distribuidos aleatoriamente. Posteriormente, focalizamos um sistema de duas bandas desordenado onde são permitidos espalhamentos intrabandas e interbandas. Este modelo é explorado com e sem campo magnético. Os resultados indicam que a universalidade do ELF nos modelos citados acima se mantém no limite de campo fraco , bastando redefinir uma constante de difusão e um tempo de relaxação efetivos. Num segundo momento, também calculamos correções em ordem 1/ N à magnetocondutividade no modelo de Wegner em três dimensões pelo método já citado, obtendo que a divergência no limite infravermerlho é eliminada pela presença do campo através da frequência de ciclotron. Um ponto importante a respeito deste modelo é a maneira como calculamos a magnetocondutividade dada a complexidade dos diagramas de Feynman que aparecem a ordem 1/ N neste modelo. Mostramos que , de maneira geral, existem duas formas equivalentes de calculo daquela quantidade (fórmula de Einstein e Abrikosov) . No entanto, pela estrutura de cada uma delas e sob certas circunstancias bem especificas, como por exemplo, os potenciais aleatórios serem. de contato, alguns diagramas que aparecem na expansão perturbativa de uma forma de cálculo (Einstein) , são suprimidos em outra (Abrikosov) , fato este que pode trazer simplificações, como é o caso concreto do modelo de Wegner em limite de campo fraco. Isto faz com que adotemos a fórmula de Abrikosov como estrategia de calculo da condutividade em todos os modelos estudados neste trabalho. / The problem of the universality of the weak localization Effect (WLE) and corrections in order 1/N to Wegner's model are studied in the presence of a magnetic field with a method based on Landau exact eigen-states according to the reference [6]. First , the magnetoconductivity of an anisotropic mass electron gas, in which the scatterer potentials are distributed randomly, was calculated. Second, it was studied a two band disordered system, in which intraband and interband scatterings are allowed. This model is explored with and without magnetic field. The results show that the WLE universality in the models mentioned before remains in the weak field limit, since an effective constant of difusion and an effective time of relaxation are redefined. After that , it were also calculated corrections in order 1/N to the magnetoconductivity in the Wegner's model in three dimensions with the method mentioned before that and the result was the divergence in the infra-red limit is eliminated by the field presence through the cyclotron frequency. Because the complexity of the Feynman diagrams in this model. it is important to highlight the way the magnetoconductivity was calculated. In general it was showed that there are two equivalent ways to calculate that quantity (Einstein and Abrikosov formulas) . Howewer, because of their structures and under certain specific circunstances, such as contact random potentials , some diagrarns which appear in the perturbative expansion of one kind of calculation (Einstein) are supressed in the other (Abrikosov) . This fact may offer some simplification, as it is the case in the Wegner model in weak field limit. For this, Abrikosov formula was used to calculate the conductivity in all the models studied in this thesis.

Ce travail est consacré à l'étude de certaines propriétés spectrales des opérateurs de Schrödinger aléatoires. Il est divisé en deux parties : 1. Une étude de la localisation d'Anderson pour des systèmes multi-particules sur un graphe quantique. 2. Une formulation abstraite de quelques estimées de Wegner, suivie par une liste d'applications pour des modèles concrets. Au Chapitre 1 on essaie d'introduire les problèmes et les résultats de la thèse de façon élémentaire. La première partie occupe les chapitres 2 et 3. Le Chapitre 2 consiste essentiellement en notre article "Anderson Localization for a multi-particle quantum graph" [97] sur le sujet. Au Chapitre 3 on discute quelques propriétés supplémentaires du modèle, et on donne surtout des démonstrations alternatives de certains résultats du Chapitre 2. La deuxième partie occupe les chapitres 4 et 5. Le Chapitre 4 reproduit essentiellement notre article "Some abstract Wegner estimates with applications" [98]. Au Chapitre 5 on poursuit l'étude des estimées de Wegner, en donnant notamment quelques théorèmes abstraits supplémentaires dans la Section 5.2 et encore d'autres applications dans la Section 5.3. On conclut avec deux annexes A et B. Dans la première on expose de manière très détaillée les développements en fonctions propres généralisées. Dans l'Annexe B, on démontre quelques résultats classiques utilisés dans le texte.

Le concept de libre arbitre semble aujourd’hui menacé par les récentes avancées neuroscientifiques. Nous examinons dans un premier chapitre le débat concernant la compatibilité du libre arbitre et du déterminisme causal. Le deuxième chapitre étudie la thèse de l’épiphénoménalisme de la conscience en recensant les données expérimentales actuellement disponibles. La théorie défendue par Daniel Wegner est analysée et donne lieu à une prise en compte des limitations de la conscience, qui sont également appuyées par la psychologie expérimentale. Ces limitations sont examinées dans une troisième partie, qui met en parallèle les notions d’inconscient cognitif et d’inconscient psychanalytique afin de permettre une redéfinition de l’action volontaire à la lumière de ces limitations. Nous défendons dans une dernière partie une approche neurophénoménologique, selon laquelle une étude de la conscience doit nécessairement passer par la prise en compte des données en première et en troisième personne, afin que ces deux types de données s’informent mutuellement. Cette démarche, qui nécessite un entraînement des capacités attentionnelles afin de décrire au mieux l’expérience vécue, permet d’envisager non seulement de nouvelles perspectives de recherche concernant la prise de décision, mais également une nouvelle définition du libre arbitre comme apprentissage. Cette redéfinition du libre arbitre s’appuie sur les études effectuées en neurosciences sur les mécanismes attentionnels, ainsi que sur l’examen des vertus thérapeutiques de certaines techniques de redirection de l’attention. / The concept of free will seems now to be threatened by recent advances in neuroscience. In the first chapter, we examine the debate concerning the compatibility of free will and causal determinism. The second chapter studies the thesis of the epiphenomenalism of consciousness by making an inventory of the experimental data currently available. The theory defended by Daniel Wegner is analyzed and leads us to take into account the limitations of consciousness, which are also supported by experimental psychology. These limitations are examined in the third chapter, in which we draw a parallel between the notions of cognitive unconscious and psychoanalytic unconscious, allowing us to redefine voluntary action in light of these limitations. In the last chapter, we defend a neurophenomenological approach, according to which a study of consciousness must necessarily take into account first-person as well as third-person data, in order for each of these types of data to inform the other. This approach, which requires a training of attentional capacities in order to best describe lived experience, allows not only to consider new research perspectives about decision making, but also a new definition of free will as an apprenticeship. This redefinition is based on neuroscientific studies about attentional mechanisms, as well as on the examination of the therapeutic virtues of certain redirection of attention techniques.

<p>This essay analyses the existence of a literary tendency in Sweden the last decade, which shares many similarities with magical realism. The study includes the work of three writers: Majgull Axelsson with Aprilhäxan; John Ajvide Lindquist with Hanteringen av odöda and Låt den rätte komma in; and finally a short story of Alejandro Leiva Wegner, “Elixir”.</p><p>Focus for this work is to expose how these writers use supernatural events/people as a strategy to create a new identity and to effect social criticism, strategies that are common to magical realism.</p><p>The aim of this work is therefore to clarify generalities about magical realism as a genre and give it a place in Swedish literature and in a changing Swedish society. Furthermore this essay defines a unique term for the genre as adapted to the Swedish reader and with some characteristics of its own: “övernaturlig realism” (supernatural realism).</p>

This essay analyses the existence of a literary tendency in Sweden the last decade, which shares many similarities with magical realism. The study includes the work of three writers: Majgull Axelsson with Aprilhäxan; John Ajvide Lindquist with Hanteringen av odöda and Låt den rätte komma in; and finally a short story of Alejandro Leiva Wegner, “Elixir”. Focus for this work is to expose how these writers use supernatural events/people as a strategy to create a new identity and to effect social criticism, strategies that are common to magical realism. The aim of this work is therefore to clarify generalities about magical realism as a genre and give it a place in Swedish literature and in a changing Swedish society. Furthermore this essay defines a unique term for the genre as adapted to the Swedish reader and with some characteristics of its own: “övernaturlig realism” (supernatural realism).