Afin de poursuivre la croissance imposée par la loi de Moore, les circuits numériques deviennent de plus en plus parallèles, avec un nombre important d'unités de calcul distinctes. L'utilisation de l'optique peut s'avérer intéressante pour leur assurer une bande passante élevée. Au contraire, les liens traditionnels (électriques) commencent à montrer leurs limites en terme de consommation par unité d'information échangée. Dans un tel contexte, il est alors nécessaire de développer des interconnexions optiques dont les procédés de fabrication restent compatibles avec le standard CMOS. Si le transport de la lumière est aisé à obtenir au voisinage de 1.55 μm avec le couple Silicium/Silice, l'obtention de sources LASER est nettement plus difficile puisque le silicium (gap indirect) ne permet pas de réaliser le gain optique requis. Une solution consiste alors à reporter par collage moléculaire des vignettes de composés à base de semi-conducteurs III-V.Dans cette thèse, nous nous intéresserons uniquement à une source bien particulière, basée sur les modes de galerie (WGM) dans les résonateurs à symétrie circulaire, de quelques micromètres de rayon. Nous verrons comment tirer profit des éléments a priori perturbateurs que sont les contacts électriques (absorbants) de sorte à diminuer le seuil LASER. La mise en place d'un modèle semianalytique permet d'obtenir un dimensionnement ultra-rapide de la source monolithique obtenue, en optimisant la géométrie et la position des électrodes de contact. La collection de la lumière dans un guide par couplage évanescent donne lieu à de complexes interactions. Là encore, une modélisation à partir de la théorie des modes couplés a permis d'en comprendre les rouages, et d'en tirer profit. Le guide lui-même peut alors servir à favoriser une seule et unique longueur d'onde d'émission. Avec des éléments actifs situés à proximité de ces guides, on peut même obtenir une source ultra-compacte et modulable dont on contrôle la longueur d'onde d'émission par un élément extérieur au LASER. La dernière partie de cette thèse fournit des résultats expérimentaux, obtenus avec une chaine "pilote" sur des wafers 200 mm (CEA LETI) en se limitant à des procédés CMOS. On démontre donc la faisabilité des sources proposées dans les chapitres précédents ainsi que la possibilité de les intégrer un lien optique complet (source, routage et détection).

In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case

Fenômenos que ocorrem a tempos curtos em sistemas quânticos abertos são caracterizados por possuírem um tempo característico de uma ordem muito menor que o tempo de relaxação do sistema. Como exemplos podemos citar o efeito de decoerência, que em resumo tenta explicar como a natureza quântica de um sistema é perdida ao longo da interação com o ambiente e o fenômeno de superradiância, onde estuda-se como alguns sistemas emitem um pulso energético muito rápido gerando um pico de intensidade fino localizado muito antes da relaxação do sistema. O objetivo desse trabalho é não só estudar esses fenômenos mas como apresentar uma técnica alternativa para a quantificação das medidas associadas e de seus tempos característicos. A técnica apresentada se baseia em fazer uma expansão perturbativa no tempo para o operador densidade a partir de uma equação mestra quântica e com seu uso calcular grandezas físicas relevantes a fenômenos que ocorrem a tempos curtos. A simplicidade da técnica e seu uso abrangente são os principais fatores motivadores deste trabalho. / Short-time phenomena in open quantum systems are characterized by having a characteristic time of a much lower order than the relaxation time of the system. As examples we can mention the effect of decoherence, which in summary tries to explain how the quantum nature of a system is lost along the interaction with the environment and the superradiance phenomenon, where is studied how some systems emit a very fast energy pulse generating a peak of fine intensity located long before the relaxation of the system. The aim of this work is not only study these phenomena but to present an alternative technique for quantifying the associated measures and their characteristic times. The presented technique is based on making a perturbative expansion in time for the density operator from a quantum master equation and use it to calculate physical quantities relevant to phenomena occurring at short times. The simplicity of the technique and its widespread use are the main motivating factors of this work.

Le but de cette thèse est l'étude des fonctions de corrélation des théries Yang-Mills dans le régime infrarouge. Il est connu que, à cause de l'invariance jauge, il est nécessaire de fixer la jauge pour calculer des valeurs moyennes analytiquement. La procedure de fixation gauge standard est la procedure de Faddeev-Popov (FP). Le Lagrangien de FP permet de faire des calculs perturbatifs pour la Chromodynamique Quantique dans le régime de hautes énergies dont les résultats sont comparés avec succès avec des expériences. Cependant, dans le régime de basses énergies, il se trouve que la constante de couplage, calculée avec la procedure antérieure, diverge. En conséquence, la théorie des perturbations standard n'est plus valide. D'autre part, les simulations du réseau trouvent que la constante de couplage est finie avec une valeur modérée même dans le régime infrarouge. Ceci suggère qu'il devrait exister une manière de faire des calculs perturbatifs également dans le régime infrarouge. Cette différence dans la constante de couplage peut être due au fait que la procedure de FP n'est pas bien justifiée dans ce régime. Nous proposons de modifier le Lagrangien de FP avec un terme massif pour les gluons. Cette modification est également justifiée par le fait que le réseau trouve un propagateur du gluon qui paraît massive aux basses énergies. Nous utilisons cette version massive pour calculer à une boucle les fonctions de corrélations à deux et trois points pour une configuration cinématique générale et en dimension quelconque dans la jauge de Landau. On trouve que les comparaisons de notre calcul à une boucle avec les résultat du réseau donnent, en géneral, un très bon accord. / The aim of this thesis is to investigate the infrared behaviour of Yang-Mills correlation functions. It is known that the gauge invariance of the theory brings as a consequence the necessity of a gauge fixing procedure in order to compute expectation values analytically. The standard procedure for fixing the gauge is the Faddeev-Popov (FP) procedure which allows one to do perturbation theory in the ultraviolet regime. Perturbative calculations using the FP gauge fixed action successfully reproduce Quantum Chromodynamics observables measured by experiments in the ultraviolet regime. In the infrared regime the coupling constant of the theory computed with the above procedure diverges, and standard perturbation theory does not seem to be valid. However, lattice simulations show that the coupling constant takes finite and not very large value. This suggests that some kind of perturbative calculations should be valid even in the infrared regime. The theoretical justification for the FP procedure depends on the absence of Gribov copies and hence is not valid in the infrared regime (where such copies exist). To correct this we propose to add a mass term for the gluons in the gauge-fixed Lagrangian. The gluon mass term is also motivated by lattice simulations which observe that the gluon propagator behaves as it was massive in the infrared regime. We use this massive extension of the FP gauge fixed action to compute the one loop correction of the two- and three-point correlation functions in the Landau gauge for arbitrary kinematics and dimension. Our one-loop calculations are enough, in general, to reproduce with good accuracy the lattice data available in the literature.

Dans cette thèse sur articles, nous nous intéressons aux grandes structures de l’Univers et à leur rôle fondamental pour la cosmologie et la formation des galaxies. Les galaxies naissent et grandissent au sein des filaments de la toile cosmique soulevant la question de l’impact de ces filaments sur les propriétés galactiques telles que la morphologie. Pour étudier cette question fondamentale, nous allons dans un premier temps montrer que dans les simulations numériques de l’Univers, le spin des galaxies est fortement lié à la direction de leur filament hôte avec un comportement qui dépend de leur masse. Ces corrélations spin-filament seront expliquées qualitativement dans le contexte de la formation hiérarchique des structures cosmologiques. Un modèle analytique tenant compte de l’anisotropie de la toile cosmique complètera ce tableau en reproduisant les corrélations observées. Ces idées sont importantes pour comprendre la morphologie des galaxies mais aussi les alignements intrinsèques qui peuvent certaines sondes cosmologiques basées sur la mesure de l’astigmatisme cosmique. Nous allons en particulier mesurer cette contamination dans une simulation hydrodynamique. Dans la seconde partie de ce manuscrit, nous nous poserons la question de comment extraire efficacement de l’information de la toile cosmique en mesurant sa topologie et sa géométrie et en utilisant la théorie perturbative dans un régime quasi-linéaire, la pierre angulaire de ce travail reposant sur l’étude analytique de l’impact de l’effondrement non-linéaire des structures et des distorsions en espace des redshifts sur la statistique du champ de densité cosmique. / This thesis by publication is devoted to the theoretical understanding of the large-scale structure of the Universe and its role in the context of cosmology and galaxy formation. The birth and evolution of galaxies occur within the large cosmic highways drawn by the cosmic web and the natural question which arises is whether galaxies retain a memory of the large-scale cosmic flows from which they emerge. To address this key question, we will first show that in cosmological simulations, the spin of galaxies and the direction of their host filament are correlated in a mass-dependent way. This signal will be shown to be qualitatively understood in the context of hierarchical structure formation. An analytic model which explicitly takes into account the anisotropy of the cosmic web will complement this qualitative understanding by reproducing the measured correlations. Those ideas are important to understand the evolution of galaxy morphology but also to understand the intrinsic alignments of galaxies that contaminate cosmological probes like cosmic shear experiments. We will in particular measure this contamination directly from a state-of-the-art hydrodynamical simulation. In a second part, we will address the question of how to efficiently use large-scale structure data to probe the cosmological model describing our Universe by measuring its topology and geometry and using perturbation theory in the weakly and even mildly non-linear regime. The major contribution of this work is to analytically study the effect of redshift space distortions and non-linear collapse of structures on the topology, geometry and statistics of the cosmic density field.

Les théories de supergravité sont des extensions supersymmetriques de la relativité générale (RG) d'Einstein. Leur comportement ultraviolet (UV) est meilleur que celui de la RG car les contributions bosoniques et fermioniques se compensent dans les diagrammes en boucles. La supergravité maximale a le meilleur comportement UV, toutefois les prédictions les plus précises venant aussi bien de la théorie des champs que de la théorie des cordes indiquent que la théorie devrait elle aussi souffrir de divergences UV, à partir de 7 boucles. Cette question ouverte constitue un cadre dans lequel peut être problématisés ma thèse. En général, l'approche que j'ai suivie consiste à étudier les amplitudes de diffusion en théorie des cordes dans la limite ou la longueur de la corde devient nulle; on s'attend ainsi à retrouver les amplitudes de diffusion de supergravité. Curieusement, on sait très peu de choses sur cette limite au délà d'une boucle. Une part importante de mon travail thèse a consisté à développer des outils mathématiques basés sur la géométrie tropicale pour décrire cette limite en genre deux et au délà. Afin de tester la précision des prédiction de la théorie des cordes, dans ma thèse j'ai aussi travaillé sur le comportement UV des théories de supergravité demi-maximale. Nous avons montré un théorème de non-renormalisation qui expliqué l'absence de divgerence à 3 boucles et en prédit une à 4 boucles. Enfin je me suis intéressé aux techniques utilisées en théorie des champs pour calculer ces amplitudes à haut nombre de boucles en théorie des champs, et notament à la "double copie BCJ", dont avons proposé la première analyse à une boucle depuis la théorie des cordes. / Supergravity theories are supersymmetric extensions of General Relativity (GR). They have a better ultraviolet (UV) behavior than GR, due to cancellations between bosons and fermions in loop diagrams. Maximal supergravity is a candidate for a UV finite point-like theory of quantum gravity. Nowadays, the most advanced understanding coming from field theory and string theory indicate that the theory should not be UV finite, and that the first UV divergences should appear at the 7-loop order. This open question constitutes a background in which my PhD thesis can be problematized.In this thesis, our approach consists in using string theory scattering amplitudes and study their point-like limit, in which supergravity amplitudes are expected to be recovered. Very little is known beyond one loop on this limit and in this manuscript I describe first how a recent field of mathematics, tropical geometry, may be used in this process, and mention some applications and open issues.Another way to cross-check the predictions of string theory on the UV behavior of maximal supergravity consists in performing the same analysis in theories of reduced supersymmetry.I discuss the case of half-maximal supergravity theories, and show a non-renormalization theorem in heterotic string which explains the vanishing of the 3-loop divergence of this theory and predicts a 4-loop divergence.The last aspect of my work is focused on a string theoretic understanding on the techniques used in field theory to compute higher loop amplitudes. I describe the first analysis of the so called BCJ double copy construction at one-loop from string theory, and partly explain the origin of the BCJ prescription.

Orientadora: Arlene Cristina Aguilar / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-31T04:21:18Z (GMT). No. of bitstreams: 1 Figueiredo_ClaraTeixeira_M.pdf: 3320128 bytes, checksum: 24dc162fc60ec8d9e4cdb7690324c5fa (MD5) Previous issue date: 2016 / Resumo: Neste trabalho, descrevemos os mecanismos de geração de uma massa dinâmica para o gluon no regime não perturbativo da QCD. Além disso, analisamos o impacto que essa geração de massa do gluon aliada ao comportamento do ghost, que permanece não massivo no região não perturbativa, causa em outras funções de Green fundamentais da QCD. A partir das equações de Schwinger-Dyson, apresentamos um formalismo teórico generalizado para lidar com a geração de massa para o gluon em teorias de Yang-Mills. A construção central se baseia na ação combinada das identidades de Ward satisfeitas pelos vértices não perturbativos (dentro do esquema PT-BFM) e uma identidade especial, chamada identidade de seagull, nos diagramas que compõem a equação de Schwinger-Dyson do propagador de gluon. O resultado dessas considerações é que o gluon permanece rigorosamente não massivo, desde que os vértices não contenham polos. Quando tais polos são incorporados aos vértices da teoria, os termos se combinam de tal forma que a aniquilação total de divergências quadráticas permanece e, ao mesmo tempo, aparecem contribuições residuais que provocam a saturação do propagador de gluon no infravermelho profundo. Esses polos se comportam como excitações de estado ligado não massivas e podem ser estudados a partir das equações de Bethe-Salpeter. As análises realizadas previamente dentro desse contexto consideravam apenas a possibilidade de polo no vértice de três gluons, desprezando efeitos advindo de possíveis polos nos demais vértices. Aqui, nós obtemos a contribuição da presença de um polo no vértice gluon-ghost para a equação dinâmica que descreve a criação de tais polos. Por fim, nota-se que o fato do gluon ganhar um massa dinâmica e o ghost permanecer não massivo impacta algumas das funções de Green da teoria, em particular o propagador de gluon e o vértice de três gluons. Assim, verificamos que o comportamento divergente dos loops de ghost induz simultaneamente um máximo no propagador de gluon e um mínimo em seu termo cinético. Além disso, esses loops provocam uma mudança de sinal e uma divergência negativa no infravermelho em um dos fatores de forma do vértice de três gluons, calculado em uma configuração cinemática especial / Abstract: In this work, we describe the mechanisms at work in the gluon dynamical mass generation in the nonperturbative regime of QCD. In addition, we obtain some effects of this mass generation allied to the behavior of the ghost, which remain massless in the nonperturbative region, in other fundamental Green's functions of QCD. From the Schwinger-Dyson equations, we present a general theoretical formalism to deal with mass generation in Yang-Mills theories. The central construction relies on the combined action of the Ward identities satisfied by the nonperturbative vertices (within the PT-BFM scheme) and a special identity, called seagull identity, in the diagrams that comprise the Schwinger-Dyson equation for the gluon propagator. The result of these considerations is that the gluon remains rigorously massless, given that the vertices do not contain poles. When such poles are incorporated to the vertices of the theory, the terms are combined in a way that the total annihilation of the quadratic divergences remains and, at the same time, residual contributions appear, which provoke the gluon propagator saturation in the deep infrared. These poles behave as massless bound-state excitations and can be studied using the Bethe-Salpeter equations. The analyses carried out previously within this context considered only the possibility of a pole in the three-gluon vertex, neglecting effects from possible poles in the remaining vertices. Here, we obtain the contribution of the presence of a pole in the gluon-ghost vertex for the dynamical equation that describes the creation of such poles. Finally, we note that the fact that the gluon gains a dynamical mass and the ghost remains massless impacts some of the Green's functions of the theory, in particular, the gluon propagator and the three-gluon vertex. Thus, we verify that the divergent behavior of the ghost loops induces simultaneously a maximum in the gluon propagator and a minimum in the kinetic term of this propagator. Besides, these loops generate a change in sign and a negative divergence in the infrared in one of the form factor of the three gluon vertex, calculated in a specific kinematic configuration / Mestrado / Física / Mestra em Física / 2014/16247-8 / 147440/2014-9 / FAPESP / CNPQ

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Dans la limite des hautes énergies, la petite valeur de la constante de couplage de l'interaction forte peut être compensée par l'apparition de grands logarithmes de l'énergie dans le centre de masse. Toutes ces contributions peuvent être du même ordre de grandeur et sont resommées par l'équation de Balitsky-Fadin-Kuraev-Lipatov (BFKL). De nombreux processus ont été proposés pour étudier cette dynamique. L'un des plus prometteurs, proposé par Mueller et Navelet, est l'étude de la production de deux jets vers l'avant séparés par un grand intervalle en rapidité dans les collisions de hadrons. Un calcul BFKL ne prenant en compte que les termes dominants (approximation des logarithmes dominants ou LL) prédit une augmentation rapide de la section efficace avec l'augmentation de l'intervalle en rapidité entre les jets ainsi qu'une faible corrélation angulaire. Cependant, des calculs basés sur cette approximation ne purent pas décrire correctement les mesures expérimentales de ces observables au Tevatron. Dans cette thèse, nous étudions ce processus à l'ordre des logarithmes sous-dominants, ou NLL, en prenant en compte les corrections NLL aux facteurs d'impact, qui décrivent la transition d'un hadron initial vers un jet, et à la fonction de Green, qui décrit le couplage entre les facteurs d'impact. Nous étudions l'importance de ces corrections NLL et trouvons qu'elles sont très importantes, ce qui conduit à des résultats très différents de ceux obtenus à l'ordre des logarithmes dominants. De plus, ces résultats dépendent fortement du choix des échelles présentes dans ce processus. Nous comparons nos résultats avec des données récentes de la collaboration CMS sur les corrélations angulaires des jets Mueller-Navelet au LHC et ne trouvons pas un bon accord. Nous montrons que cela peut être corrigé en utilisant la procédure de Brodsky-Lepage-Mackenzie pour fixer le choix de l'échelle de renormalisation. Cela conduit à des résultats plus stables et une très bonne description des données de CMS. Finalement, nous montrons que, à l'ordre des logarithmes sous-dominants, l'absence de conservation stricte de l'énergie-impulsion (qui est un effet négligé dans un calcul BFKL) devrait être un problème beaucoup moins important qu'à l'ordre des logarithmes dominants. / In the high energy limit of QCD, the smallness of the strong coupling due to the presence of a hard scale can be compensated by large logarithms of the center of mass energy. All these logarithmically-enhanced contributions can be resummed by the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Many processes have been proposed to study these dynamics. Among the most promising ones is the production of two forward jets separated by a large interval of rapidity at hadron colliders, proposed by Mueller and Navelet. A BFKL calculation taking into account only dominant contributions (leading logarithmic, or LL, accuracy) predicts a strong rise of the cross section with increasing rapidity separation between the jets and a large decorrelation of their azimuthal angles. However, such LL calculations could not successfully describe measurements of these observables performed at the Tevatron. In this thesis, we study this process at next-to-leading logarithmic (NLL) accuracy, taking into account NLL corrections both to the impact factors, which describe the transition from an incoming hadron to a jet, and to the Green's function, which describes the coupling between the impact factors. We investigate the magnitude of these NLL corrections and find that they are very large, leading to very different results compared with a LL calculation. In addition, we find that these results are very dependent on the choice of the scales involved in the process. We compare our results with recent data from the CMS collaboration on the azimuthal correlations of Mueller-Navelet jets at the LHC and find a rather poor agreement. We show that this can be cured by using the Brodsky-Lepage-Mackenzie procedure to fix the renormalization scale. This leads to more stable results and a very good description of CMS data. Finally, we show that at NLL accuracy the absence of strict energy-momentum conservation (which is a subleading effect in a BFKL calculation) should be a much less severe issue than at LL accuracy.

A passagem progressiva de estados de Landau bidimensional (2D) para estados tridimensional (3D) foi estudada em Poços Quânticos Parabólicos (PQW) largos (W = 1000 6000 Å). Utilizou-se como técnica de transporte medidas da magnetoresistência em campo magnético intenso (B = 0 15 T) e inclinado ( = 0 90°; perpendicular paralelo), a baixas temperaturas (T = 50 mK). Observou-se, através da dependência angular das oscilações de Shubnikov de Haas ( = 0 90°), em PQWs cheios, várias sub-bandas ocupadas (5 a 8), a coexistência de estados de Landau 2D e 3D, sendo o gás 3D formado pelo colapso das sub-bandas elevadas, e o gás 2D pertencendo à primeira sub-banda. Através de cálculos do alargamento dos níveis de Landau devido ao espalhamento elástico ( = /2 , onde é o tempo quântico) e de cálculos auto-consistentes da energia de separação entre sub-bandas do PQW (ij = Ej Ei; e 12=12/2), obtiveram-se as condições 2 j-1,j para as sub-bandas elevadas j = 3,4,..., corroborando com as observações experimentais da coexistência de estados de Landau 2D e 3D no poço. Em PQWs parcialmente cheios, com apenas 2 sub-bandas ocupadas, observou-se, através do efeito do anticruzamento de níveis de Landau, de medidas da dependência angular da energia de ativação no regime de efeito Hall quântico, e de comparações com resultados de cálculos da estrutura eletrônica de PQWs em campo magnético inclinado, a coexistência de estados de Landau 2D e 3D, ocorrendo somente em campos intensos e com inclinação acentuada ( = 80 90°). Esta coexistência é diferente da mencionada anteriormente, quando od estados de Landau 3D são observados já em campo perpendicular. / The gradual progress, or evolution, of the two-dimensional (2D) toward three-dimensional (3D) Landau states was studied in wide parabolic quantum Wells (W = 1000 6000 Å). As transport technique, we used measurements of the magnetoresistence in intense (B = 0 15 T) and tilted ( = 0 90°; perpendicular parallel) magnetic Field at low temperature (T = 50 Mk). We observed in PQWs with Five to eight sub-bands occupied full well the coexistence of the 2D and 3D Landau states, through the angular dependence of the Shubnikov de Hass oscillation ( = 0 90°), where the 2D states belong to the lowest sub-band and the 3D states are formed by overlap of the other sub-bands. We calculated the level broadening due to the elastic scattering rate ( = /2 , where is the quantum time), and the energy separation between sub-bands (ij = Ej Ei; e 12=12/2). We obtained 2 j-1,j to j=3,4,... . This confirms the experimental observations of the coexistence of the 2D and 3D states in the well. We also measured PQWs partially full 2 sub-bands occupied. Experiments revel anticrossing of the Landau level (LL) belonging to the lowest sub-band and the last LL belonging to the second sub-band. Such antisrossuing occurs due to a decrease of the energy of the LL with tilt angle. This observation was supported by measurements of the angular dependence of the activation energy in the quantum Hall regime. In these measurements, we also observed the coexistence of the 2D and 3D Landau states. However, the coexistence only occurs at large tilt angles ( = 80 90°). Thus, it is different from the coexistence above mentioned, when 3D Landau states are observed already in the perpendicular magnetic field.