As teorias de gravitação invariante por escala propõem uma variação com relação ao tempo da constante gravitacional ou da massa dos objetos que constituem o universo. Desta forma a intensidade da interação gravitacional também se torna variável, modificando sensivelmente o comportamento do universo. Algumas teorias foram propostas no decorrer do século, porém, descartadas devido a problemas técnicos e de concordância com dados observacionais. trabalho a ser apresentado nesta dissertação está fundamentado em uma teoria de gravitação invariante por escala, a qual vem atualmente sendo desenvolvida e é denominada teoria penta-dimensional Espaço-Tempo-Massa. Tal teoria propõe a quantidade de massa de repouso como uma quantidade extensiva, de maneira a introduzi-la na métrica e torná-la variável. Diversos trabalhos foram realizados com esta teoria, incluindo alguns, o estudo de modelos cosmológicos. Investigaremos aqui a extensão do modelo cosmológico de Bianchi tipo V, que é um dos mais importantes modelos do universo. Duas métricas foram propostas e as soluções das equações de campo da teoria SD-Espaço-Tempo-Massa para tais métricas foram obtidas. Tais soluções correspondem a espaços não-planos. Um estudo sobre singularidades na métrica e na curvatura foi realizado para ambas as métricas, em adição, o tensor de energia-momento induzido foi obtido para as métricas e as suas propriedades investigadas. Através da análise do tensor de Kretschmann verificou-se a ausência de singularidades efetivas nos modelos 5D abordados, sugerindo uma distribuição finita de energia devido a inclusão da massa de repouso. / The scale invariant gravitational theories propose the time variation either in the gravitational constant or in the rest mass of the objects that constitute the universe. By this way the intensity of the gravitational interaction varies as well, changing accordingly the behavior of the universe. Several theories have been proposed in the literature, however most of them have been discharged due to drawbacks in thecnicalities or lack of agreement with observational data. The work conducted here takes into account a 5-dimensional theory called SpaceTime- Mass, which proposes that the rest mass be na extensible quantity that change with time. Severa! investigations have been done so far with this theory, some o f them including cosmological studies. Here we will investigate the 5D extension of the Bianchi type V cosmological model, which is one of the most important model of the universe. Two metrics are proposed and the solution of the corresponding 5D-Spae-Time-Mass field equations are found. Both solutions shown to be non-flat spaces. The singularity behavior of the metric and curvature were done, the induced energy-momentum tensor for both metrics were determined and their properties were investigated. Through the analysis of the Kretschmann tensor, it has been shown that there is no effective singularity in the space, which suggest that there is a finite distribution of energy due to the inclusion of the rest mass variable.

As teorias de gravitação invariante por escala propõem uma variação com relação ao tempo da constante gravitacional ou da massa dos objetos que constituem o universo. Desta forma a intensidade da interação gravitacional também se torna variável, modificando sensivelmente o comportamento do universo. Algumas teorias foram propostas no decorrer do século, porém, descartadas devido a problemas técnicos e de concordância com dados observacionais. trabalho a ser apresentado nesta dissertação está fundamentado em uma teoria de gravitação invariante por escala, a qual vem atualmente sendo desenvolvida e é denominada teoria penta-dimensional Espaço-Tempo-Massa. Tal teoria propõe a quantidade de massa de repouso como uma quantidade extensiva, de maneira a introduzi-la na métrica e torná-la variável. Diversos trabalhos foram realizados com esta teoria, incluindo alguns, o estudo de modelos cosmológicos. Investigaremos aqui a extensão do modelo cosmológico de Bianchi tipo V, que é um dos mais importantes modelos do universo. Duas métricas foram propostas e as soluções das equações de campo da teoria SD-Espaço-Tempo-Massa para tais métricas foram obtidas. Tais soluções correspondem a espaços não-planos. Um estudo sobre singularidades na métrica e na curvatura foi realizado para ambas as métricas, em adição, o tensor de energia-momento induzido foi obtido para as métricas e as suas propriedades investigadas. Através da análise do tensor de Kretschmann verificou-se a ausência de singularidades efetivas nos modelos 5D abordados, sugerindo uma distribuição finita de energia devido a inclusão da massa de repouso. / The scale invariant gravitational theories propose the time variation either in the gravitational constant or in the rest mass of the objects that constitute the universe. By this way the intensity of the gravitational interaction varies as well, changing accordingly the behavior of the universe. Several theories have been proposed in the literature, however most of them have been discharged due to drawbacks in thecnicalities or lack of agreement with observational data. The work conducted here takes into account a 5-dimensional theory called SpaceTime- Mass, which proposes that the rest mass be na extensible quantity that change with time. Severa! investigations have been done so far with this theory, some o f them including cosmological studies. Here we will investigate the 5D extension of the Bianchi type V cosmological model, which is one of the most important model of the universe. Two metrics are proposed and the solution of the corresponding 5D-Spae-Time-Mass field equations are found. Both solutions shown to be non-flat spaces. The singularity behavior of the metric and curvature were done, the induced energy-momentum tensor for both metrics were determined and their properties were investigated. Through the analysis of the Kretschmann tensor, it has been shown that there is no effective singularity in the space, which suggest that there is a finite distribution of energy due to the inclusion of the rest mass variable.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-06T13:06:24Z No. of bitstreams: 2 Dissertação - Hugo Leonardo Carvalhaes Couto - 2014.pdf: 4274634 bytes, checksum: b9959e074591eac4834096b0e3695781 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-06T13:09:34Z (GMT) No. of bitstreams: 2 Dissertação - Hugo Leonardo Carvalhaes Couto - 2014.pdf: 4274634 bytes, checksum: b9959e074591eac4834096b0e3695781 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-03-06T13:09:34Z (GMT). No. of bitstreams: 2 Dissertação - Hugo Leonardo Carvalhaes Couto - 2014.pdf: 4274634 bytes, checksum: b9959e074591eac4834096b0e3695781 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / (Sem resumo em outra língua) / Sólitons são estruturas que se propagam em sistemas não lineares sem se dispersarem. Os sólitons escuros formam um tipo específico de sólitons caracterizados por uma depressão na densidade do campo e por uma variação repentina da fase na região da depressão. O estado de condensação de Bose-Einstein em gases atômicos fracamente interagentes obedece de maneira aproximada à equação não linear de Schrödinger conhecida por Equação de Gross- Pitaevskii (EGP). Estudos teóricos e experimentais revelam que sólitons escuros propagando em condensados de Bose-Einstein (BEC) são instáveis. Quando o BEC tem geometria quaseunidimensional, a principal fonte de instabilidade na dinâmica do sóliton é a interação sólitonsom, responsável pelo decaimento e pela eventual perda do sóliton. O modelo cúbico, dentre todas as reduções dimensionais da EGP para uma dimensão, é o modelo mais frequentemente usado para o estudo desses sistemas. Em 2008 [1], Muñoz Mateo e Delgado propuseram um modelo mais preciso que o modelo cúbico e que os principais modelos unidimensionais propostos até então. No presente trabalho comparamos a dinâmica e o decaimento de sólitons escuros em BECs segundo os modelos cúbico e de Muñoz Mateo e Delgado (MMD). Avaliamos as diferenças relevantes nas trajetórias e nos tempos de vida dos sólitons e em que condições ocorrem.

In the thesis, we set out to study a certain class of algebraically special spacetimes in arbitrary dimension. These are the so-called spacetimes of Weyl and traceless Ricci type N. Our work can be divided into two parts. In the first part, we study general geometrical properties of spacetimes under consideration. In particular, we are interested in various properties of aligned null directions - certain significant null directions associated with algebraic structure of the Weyl and the Ricci tensor. Since the obtained results are of geometric nature, they are theory-independent and thus hold in Einstein's gravity as well as in its various generalizations. In the second part of our work, we apply these general results in the Einstein-Maxwell p-form theory, within which spacetimes of traceless Ricci type N emerge naturally as a part of a solution of the Einstein-Maxwell equations with a null Maxwell field. Powered by TCPDF (www.tcpdf.org)

[pt] Poeta de vanguarda, historiador e teórico da arte, Carl Einstein (1885-1940) foi mediador cultural entre França e Alemanha, cofundador da revista Documents (1929) junto com George Bataille, Michel Leiris, Georges Wildenstein e George-Henri Rivière. Pertenceu ao círculo de Daniel-Henry Kahnweiler, conheceu Picasso, Braque, Gris e Léger. Uma compreensão do cubismo para além da pintura, uma história da arte como luta de experiências ópticas, espaços inventados e figurações e a reformulação de conceitos enraizados na tradição alemã são alguns aspectos que caracterizam seu pensamento. Por um lado, um cubismo que não remete à representação do objeto e sim a um processo visual e mental por parte do artista e do observador, no qual o objeto é o resultado desse duplo processo. Por outro, uma escrita engajada o leva a encerrar o Georges Braque (1934) com a frase o mito foi reintegrado ao real, e a poesia se torna o elemento originário da realidade. A reintegração do mito enquanto criação de realidade, e a poiesis, ação que transforma e da sentido ao mundo, são as alternativas introduzidas por Carl Einstein para uma arte, e uma história da arte, que não considere os objetos como reflexo do mundo exterior e sim como criadores do mundo exterior dos homens. O objetivo desta tese é acompanhar e analisar sua relação com a Kunstwissenschaft, assim como as transformações às quais submete os conceitos, para assim apreender a singularidade do seu pensamento. / [en] Avant-garde poet, historian and art theorist, Carl Einstein (1885-1940) was a cultural actor between France and Germany as well as co-founder of Documents (1929), together with George Bataille, Michel Leiris, Georges Wildenstein and George-Henri Riviere. He was part of Daniel-Henry Kahnweiler’s circle and kept friendship with Picasso, Braque, Gris and Léger. His understanding of Cubism as a process beyond painting, his approach of art history as the struggle of optical experiences, invented spaces figurations, his reformulation of concepts deeply rooted in the German tradition are some of the aspects that characterize the originality of his thought. On one hand, the Cubist proposal does not imply a representation of the object, but a visual and mental process undergone by both the artist and the observer where the object is the result of this dual process. On the other, an engagement with language drove Einstein to end his Georges Braque (1934) with the phrase myth was reintegrated to the Real, and poetry becomes the originating element of reality. Restoring myth as a means for the creation of reality, and poiesis, an action that transforms and gives sense to the world, are the alternatives introduced by Carl Einstein into an art, and art history, which does not consider objects as reflection of an outside world but as creators of the outer world of men. This dissertation follows and analyzes Einsteins relationship with the discipline known as Kunstwissenschaft and the transformations to which he submitted some of its concepts in order to understand the singularity of his thought.

In recent years, improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to detect variations of fundamental constants in precision atomic clocks. Now in our experiment we investigate how the two systems can be advantageously combined. We immerse a single trapped Yb+ ion in a Bose-Einstein condensate of Rb atoms. Our hybrid setup consists of a linear RF-Paul trap which is overlapped with a magnetic trap and an optical dipole trap for the neutral atoms. A first synergetic effect is the sympathetic cooling of the trapped ions to very low temperatures through collisions with the ultracold neutral gas and thus without applying laser light to the ions. We observe the dynamics of this effect by measuring the mean ion energy after having an initially hot ion immersed into the condensate for various interaction times, while at the same time monitoring the effects of the collisions on the condensate. The observed ion cooling effect calls for further research into the possibility of using such hybrid systems for the continuous cooling of quantum computers. To this end a good understanding of the fundamental interaction processes between the ion and the neutrals is essential. We investigate the energy dependent elastic scattering properties by measuring neutral atom losses and temperature increase from an ultracold thermal cloud of Rb. By comparison with a Monte-Carlo simulation we gain a deeper understanding of how the different parameters affect the collisional effects. Additionally, we observe charge exchange reactions at the single particle level and measure the energy-independent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.

Probing nonequilibrium dynamics in a trapped, inhomogeneous atomic quantum gas can be a challenging task because coexisting mass transport and spreading of quantum correlations often make the problem intractable. By removing density inhomogeneity in an atomic quantum gas and employing local control of chemical potential as well as interaction parameters, it is possible to perform quasi-particle control, initiate and probe collective quantum dynamics without or with a controlled mass flow. We report our experimental results toward quasi-particle control and nonequilibrium dynamics in a homogeneous two-dimensional quantum gas.

Dans ce manuscrit, nous présentons une étude expérimentale du phénomène de compression de spin dans un condensat de Bose-Einstein de $^{87}Rb$, résultant d'une interaction non-linéaire provenant de collisions entre les deux états internes $|F=1, m_F=-1>$ et $|F=2, m_F=1>$ de l'état fondamental $5^2S_{1/2}$. Les atomes sont refroidis dans un piège magnéto-optique, puis piégés magnétiquement à l'aide de notre puce à atomes jouant le rôle de parois supérieure pour notre enceinte à vide. La puce est aussi utilisée pour émettre le champ radiofréquence permettant le refroidissement évaporatif conduisant à la condensation de Bose-Einstein, ainsi que le champ micro-onde qui réalise le transfert cohérent des atomes d'un état interne à un autre.L'ensemble atomique est décrit par le Hamiltonien "textit{one-axis-twisting}" qui contient un terme quadratique en la composante selon l'axe $z$ du vecteur de spin atomique $S_z$. L'amplitude de cette interaction non-linéaire, initialement très faible, dépend des longueurs de diffusion des états internes considérés, et peut être grandement augmentée en réduisant le recouvrement des fonctions d'onde. C'est pourquoi le système est placé dans une configuration particulière (grand nombre d'atomes et piège anisotrope de type "cigare") pour laquelle les deux états vont alterner des phases de séparation et recombinaison spatiale. L'impact de cette dynamique spatiale sur l'interaction de champ moyen et la cohérence du système est analysé expérimentalement à travers l'étude du contraste et de la fréquence centrale d'un interféromètre de Ramsey.Théoriquement, lorsque les deux états sont séparés, la distribution de spin se transforme d'une distribution circulaire régie par le bruit de projection quantique, en une ellipse dont le petit axe est inférieur à la limite quantique standard, sous l'effet de l'interaction en $S_z^2$. Ceci est vérifié expérimentalement en réalisant la tomographie de l'état atomique au moment où les deux modes internes se recombinent. Un paramètre de compression de spin $xi^2 = -1.3 pm 0.4$ dB est ainsi obtenu pour 5000 atomes et un contraste de 90%. L'étude des différentes sources d'instabilités a permis d'identifier les pertes atomiques comme limitation principale de la compression de spin et du contraste de l'interféromètre.Ce travail s'inscrit dans le contexte de la métrologie quantique et représente un pas vers la production d'états comprimés en spin permettant la réalisation d'interféromètres atomiques fonctionnant sous la limite quantique standard. La question de la cohérence d'un condensat bimodal soumis à de nombreuses collisions élastiques et inélastiques est aussi adressée. / In this manuscript, we present an experimental study of spin squeezing in a spinor Bose-Einstein condensate of $^{87}Rb$, arising from a non-linear interaction originating from collisions between the two internal states $|F=1, m_F=-1>$ and $|F=2, m_F=1>$ of the $5^2S_{1/2}$ manifold. The atoms are cooled down in a magneto-optical trap and magnetically trapped thanks to our atom-chip which acts as a top wall for our vacuum cell. The chip is also used to emit the radio-frequency field that perform the evaporative cooling leading to Bose-Einstein condensation, and the microwave field used to coherently transfer the atoms from one internal state to another.The atomic ensemble in a coherent superposition is well described by the so-called textit{one-axis-twisting} Hamiltonian that contains a term quadratic in the $z$-component of the spin vector $S_z$. the strength of this non-linear interaction, initially very weak, depends on the intra- and inter-state s-wave scattering lengths, and can be greatly enhanced by reducing the wave-function spatial overlap between the two states. We therefore place the system in a configuration (high atom number and cigar-shaped trap) for which the two states experience spontaneous relative spatial separation and recombination phases. The impact of this spatial dynamics on the mean field interaction and coherence of the system is experimentally analyzed through the study of the contrast and central frequency of a Ramsey interferometer.Theoretically, when the two states are separated, the spin noise distribution evolves from a uniform circular distribution defined by the quantum projection noise, to an elliptic one whose small axis is smaller than the standard quantum limit, under the action of the $S_z^2$ interaction. This is verified experimentally by performing the tomography of the atomic state, when the two internal modes recombine. A squeezing parameter $xi^2=-1.3 pm 0.4$ dB is reached for 5000 atoms and a 90% contrast. The study of the different instability sources highlights the atomic-density-dependent losses as the main limitation for both the noise reduction and the contrast of the interferometer.This work has been initiated in the context of quantum metrology and represents a step towards the production of spin squeezed states enabling the realization of atom interferometers working below the standard quantum limit. It also addresses the fundamental question of coherence of spinor Bose-Einstein condensates undergoing many elastic and inelastic collisions.

Ce mémoire de recherche-création explore les différentes modalités de la représentation d’une théorie scientifique—la théorie de la relativité, développée par Albert Einstein au début du XXe siècle—et se concentre sur le voyage dans le temps. Le mémoire est divisé en deux parties : un texte de recherche et un projet de création. Dans le texte de recherche, le premier chapitre rappelle ce qu’est la théorie de la relativité et fait un bref historique des films sur le voyage dans le temps; le second chapitre est une analyse du film Interstellar réalisé par Christopher Nolan en collaboration avec le physicien américain, Kip Thorne. Dans ce film, la théorie de la relativité n’est pas un élément secondaire, mais le coeur même de l’histoire. Ma création, présentée ici dans un document de jeu (Concept narratif d’un jeu vidéo), est un projet de jeu vidéo se déroulant pendant la seconde guerre mondiale, dans lequel le joueur devra voyager dans le temps pour sauver l’humanité du pouvoir nazi. / This research-creation master’s thesis explores the different modalities of the representation of the Theory of Relativity, developed by Albert Einstein in the beginning of the 20th century and focuses on time travel. The dissertation is divided into two parts: a research essay and a creation project. The first chapter of the research explains the basis of the Theory of Relativity and gives a brief history of time-travel in cinema. The second chapter analyses the movie Interstellar, produced by Christopher Nolan in collaboration with the American physicist Kip Thorne. This motion picture is a prime example of the Theory of Relativity in modern cinema. The creation section, presented here in a Video game narrative concept, is a video game project set during the Second World War, in which the player will have to travel through time in order to save humanity from the Nazis.