The Lorentz gas model describes a cloud of noninteracting point particles in an infinitely extended array of spherical scatterers with centers in a given locally finite point set of uniform density. In the classical case of identical scatterers, Marklof and Strömbergsson have recently developed a general framework that derives the macroscopic transport equations of this gas for a large class of such point sets. This master's thesis is part of a forthcoming paper by the author that generalizes this framework so as to allow non-identical scatterers. Under certain conditions on the point set and on the distribution of scatterer types, we prove a limit theorem for the free path length and the parameters of the first collision. We also establish bounds on the probability of grazing a scatterer, and sketch how this knowledge gives control of the flight process in the macroscopic limit. As an application, we show that our hypotheses hold for finite unions of affine lattices with one scatterer type per lattice, generalizing a recent result of Palmer and Strömbergsson.

La matière dense et tiède (WDM) est un régime caractérisé par une densité proche du solide pour une température avoisinant celle de Fermi. Pour étudier cet état de la matière, dans cette thèse, une expérience d'interférométrie dans le domaine des fréquences est mise en place afin de mesurer la phase et la réflectivité - dans les deux directions de polarisation S et P - d'une onde sonde en réflexion sur un échantillon chauffé de manière très brève par une impulsion laser ultra-courte (sub-100fs). Il est alors porté dans un état hors-équilibre. Une méthode basée sur les mesures de réflectivité est mise en place pour contrôler la forme de l'interface entre le vide et la matière chauffée. Pour des fluences laser de l'ordre de 1 J/cm2, l'hydrodynamique d'un échantillon chauffé est étudiée par la mesure du déplacement de la surface et comparée au code hydrodynamique à deux températures ESTHER. Ensuite, la fonction diélectrique à 800 nm et 400 nm est déduite des mesures expérimentales et certaines quantités en sont extraites comme la densité électronique, la température électronique et les fréquences de collision en régime WDM. Elles sont par la suite comparées avec des modèles couramment utilisés. / The Warm Dense Matter (WDM) regime is characterised by a density close to the solid density and an electron temperature close to the Fermi temperature. In this work, the nonequilibrium Warm Dense Matter is studied during the solid to liquid phase transition induced by an ultra short laser interacting with a solid. A 30 femtoseconds time resolution pump-probe experiment (FDI) is set up, yielding to the measurement of the heated sample complex reflectivity for both S and P polarisation.We have determined a criterion based on the measured reflectivities, which permits to control the interface shape of the probed matter. For pump laser fluences around 1 J/cm2, the hydrodynamics of the heated matter is studied and experimental results are compared to the two-temperatures code ESTHER. Furthermore, the evolution of the dielectric function at 800 nm and 400 nm is inferred from our measurements on a sub-picosecond time-scale. Within the Drude-Lorentz model for the conduction electrons, the dielectric function yields information such as ionisation state, electronic temperature and electron collision frequency.

Using interpolation methods, new results on the boundedness of quasilinear joint weak type operators on Lorentz-Karamata (LK) spaces are established. LK spaces generalize many function spaces introduced before in literature, for example, the generalized Lorentz- Zygmund spaces, the Zygmund spaces, the Lorentz spaces and, of course, the Lebesgue spaces. The focus is mainly on the limiting cases of interpolation, where the spaces involved are, in certain sense, very close to the endpoint spaces. The results contain both necessary and sufficient conditions for the boundedness of the given operator on LK spaces. The complete characterization of embeddings of LK spaces is also included and the optimality of achieved results is then discussed. Finally, we apply our results to the conjugate function operator, which is known to be bounded on $L_p$ only if $1<p<\infty.$ Powered by TCPDF (www.tcpdf.org)

Relativity is one of the most important and well tested theories and Lorentz invariance is one of its pillars. Lorentz invariance violation (LIV), however, has been discussed in several quantum gravity and high energy models. For this reason, it is crucial to test it. Several tests, both terrestrial and astrophysical, have been performed in the last years and provide limits on the violation. This work takes part in these efforts and discuss the possibility of testing LIV with ultra-high energy cosmic rays (UHECRs). The effects of LIV in their propagation and the resulting changes in the spectrum of UHECRs are obtained and compared to the experimental data from the Pierre Auger Observatory. An analytical calculation for the inelasticity in the laboratory frame with LIV of any a + b &rarr; c + d interaction is presented and used to obtain the phase space and the energy losses of the pion production for protons, the photodisintegration for nuclei and the pair production for photons with LIV. A parametrization for the threshold energy of the photodisintegration with LIV is also proposed. The main effect seen is a decrease in the phase space and a resulting decrease in the energy loss. These changes have been implemented in Monte Carlo propagation codes and the resulting spectra of protons, nuclei and photons on Earth have been obtained and fitted to the data from the Pierre Auger Observatory. It is shown that upper limits on the photon LIV coefficient can be derived from the upper limits on the photon flux from the Pierre Auger Observatory. / Relatividade é uma das mais importantes e bem testadas teorias e a invariância de Lorentz é um de seus pilares. A violação da invariância de Lorentz (VIL), todavia, tem sido discutida em diversos modelos de gravidade quântica e altas energias. Por tal motivo, é crucial testá-la. Diversos testes, tanto terrestres quanto astrofísicos, foram realizados nos últimos anos e fornecem limites na violação. Este trabalho se insere nesses esforços e discute a possibilidade de testar VIL com raios cósmicos de altíssima energia. Os efeitos da VIL em sua propagação e as consequentes mudanças no espectro de raios cósmicos de altíssima energia são obtidos e comparados com os dados experimentais do Observatório Pierre Auger. Um cálculo analítico para a inelasticidade no referencial do laboratório com VIL para qualquer interação da forma a + b &rarr; c + d é apresentado e usado para obter o espaço de fase e as perdas de energia para a produção de píons para prótons, a fotodesintegração para núcleos e a produção de pares para fótons com VIL. Uma parametrização para o limiar de energia da fotodesintegração com VIL também é proposta. O principal efeito observado é uma diminuição no espaço de fase e uma consequente diminuição nas perdas de energia. Tais mudanças foram implementadas em códigos de Monte Carlo para a propagação e os espectros resultantes para prótons, núcleos e fótons na Terra foram obtidos e ajustados aos dados do Observatório Pierre Auger. É mostrado que limites superiores nos coeficientes de VIL para o fóton podem ser deduzidos dos limites superiores para o fluxo de fótons do Observatório Pierre Auger.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-12-04T14:44:31Z No. of bitstreams: 1 João Andrade..pdf: 3163183 bytes, checksum: 0c7d19f31b8e570d13e85b371ea43554 (MD5) / Made available in DSpace on 2017-12-04T14:44:31Z (GMT). No. of bitstreams: 1 João Andrade..pdf: 3163183 bytes, checksum: 0c7d19f31b8e570d13e85b371ea43554 (MD5) Previous issue date: 2017-02-22 / CAPES. / For the recent years, there has been a growing interest in Lorentz-violating theories. Studies have been carried out addressing the inclusion of Lorentz-violating terms into the Standard Model (SM). This has led to the development of the Standard Model Extension (SME), which is a framework containing modifications that are power-counting renormalizable and consistent with the gauge structure of the SM. More recently, a nonminimal version of the SME was developed for the photon, neutrino, and fermion sector additionally including higher-derivative terms. One of the new properties of this nonminimal version is the lost of renormalizability. In this work, we study the main aspects of a modified Dirac theory in the nonminimal Standard-Model Extension. We focus on two types of operators namely, pseudovector and two-tensor operators. These two operators display an unusual property; they break the degeneracy of spin. This new property becomes manifest in providing two di erent dispersion relations, one for each spin projection. To solve the Dirac equation modified by those operators, we introduce a new method that was suggested by Kostelecký and Mewes in a recent research paper. This method allows to block-diagonalizing the modified Dirac equation and, thus, permits us to obtain the spinors. The objectives of the current work are as follows. First, we will review the main concepts for understanding the SME. Second, we will introduce how to extend the minimal fermion sector to the nonminimal one. Third, we will describe the method that block-diagonalizes the modified Dirac equation and we will compute the field equations. And,finally, we will get the exact dispersion relations and the spinor solutions for operators of arbitrary mass dimension. / Nos últimos anos, houve um aumento significativo no interesse em teorias que violam a simetria de Lorentz. Estudos têm sido realizados na tentativa de incluir termos que violam a simetria de Lorentz no Modelo Padrão (MP). Esta tentativa culminou no surgimento do chamado Modelo Padrão Estendido (MPE). Este modelo contempla todas as possíveis modificações que são consistentes com as propriedades já bem estabelecidas, tais como renormalizabilidade e a estrutura de gauge do MP. Mais recentemente, uma versão não-mínima do MPE foi desenvolvida para os setores dos fótons, neutrinos e para os férmions. Esta versão não-mínima caracteriza-se pela presença de altas derivadas. Uma das novas propriedades nesta versão não-mínima é a perda da renormalizabilidade. Neste trabalho, estudamos os principais aspectos da teoria de Dirac modi cada no MPE não-mínimo. Nós nos concentramos em dois tipos de operadores a saber, operadores pseudovetoriais e tensoriais. Estes dois operadores exibem uma propriedade incomum, eles quebram a degenerescência de spin. Esta nova propriedade manifesta-se, por exemplo, na presença de duas relações de dispersão diferentes, uma para cada projeção do spin. Para resolver a equação de Dirac modi cada por esses operadores, introduzimos um novo método que foi sugerido por Kostelecký e Mewes em um trabalho recente. Este método permite bloco-diagonalizar a equação de Dirac modi cada e, assim, nos fornece uma nova maneira de obter os espinores. Os objetivos do presente trabalho são os seguintes. Primeiro, iremos rever alguns conceitos essenciais para o entendimento do MPE. Segundo, apresentaremos a extens ão do setor fermiônico mínimo para o não-mínimo. Terceiro, descreveremos o método que bloco-diagonaliza a equação de Dirac modi cada e calcularemos as equações de campo. Por fim, calcularemos as relações de dispersão exatas e as soluções espinoriais para cada configuração não-mínima dos operadores citados.

Cette thèse étudie deux modèles de calcul: les marches quantiques (QW) et les automates cellulaires quantiques (QCA), en vue de les appliquer en simulation quantique. Ces modèles ont deux avantages stratégiques pour aborder ce problème: d'une part, ils constituent un cadre mathématique privilégié pour coder la description du système physique à simuler; d'autre part, ils correspondent à des architectures expérimentalement réalisables.Nous effectuons d'abord une analyse des QWs en tant que schéma numérique pour l'équation de Dirac, en établissant leur borne d'erreur globale et leur taux de convergence. Puis nous proposons une notion de transformée de Lorentz discrète pour les deux modèles, QW et QCA, qui admet une représentation diagrammatique s'exprimant par des règles locales et d'équivalence de circuits. Par ailleurs, nous avons caractérisé la limite continue d'une grande classe de QWs, et démontré qu'elle correspond à une classe d'équations aux dérivées partielles incluant l'équation de Dirac massive en espace-temps courbe de $(1+1)$-dimensions.Finalement, nous étudions le secteur à deux particules des automates cellulaires quantiques. Nous avons trouvé les conditions d'existence du spectre discret (interprétable comme une liaison moléculaire) pour des interactions à courte et longue portée, à travers des techniques perturbatives et d'analyse spectrale des opérateurs unitaires. / This thesis is devoted to the development of two well-known models of computation for their application in quantum computer simulations. These models are the quantum walk (QW) and quantum cellular automata (QCA) models, and they constitute doubly strategic topics in this respect. First, they are privileged mathematical settings in which to encode the description of the actual physical system to be simulated. Second, they offer an experimentally viable architecture for actual physical devices performing the simulation.For QWs, we prove precise error bounds and convergence rates of the discrete scheme towards the Dirac equation, thus validating the QW as a quantum simulation scheme. Furthermore, for both models we formulate a notion of discrete Lorentz covariance, which admits a diagrammatic representation in terms of local, circuit equivalence rules. We also study the continuum limit of a wide class of QWs, and show that it leads to a class of PDEs which includes the Hamiltonian form of the massive Dirac equation in (1+1)-dimensional curved spacetime.Finally, we study the two particle sector of a QCA. We find the conditions for the existence of discrete spectrum (interpretable as molecular binding) for short-range and for long-range interactions. This is achieved using perturbation techniques of trace class operators and spectral analysis of unitary operators.

Made available in DSpace on 2016-12-08T15:56:18Z (GMT). No. of bitstreams: 1 Luiz Antonio Alves.pdf: 4887074 bytes, checksum: 2921556dad24ae9311fe651e5a0ccdcf (MD5) Previous issue date: 2014-07-14 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Titanium nitride (TiN) films with niobium (Nb) addition (TiN[Nb], 0,01 < Nb/Ti < 0,15) were obtained by sputter deposition in a triode magnetron sputtering system from a mosaic target of titanium with niobium inserts at the erosion zone. The effects of Nb/Ti in surface morphology were analyzed by atomic force and confocal microscopy measurements. The reflectivities of the films with niobium incorporation are in agreement with the Drude-Lorentz model. The constants obtained by the fitting show an increase in plasma frequency and relaxation time with increased Nb/Ti ratio, indicating an increase in the number of charge carriers. The color parameters according CIELab system show an increase in L*, a* and b* coordinates. The visual analysis indicates an increased red tone when compared with pure TiN film in agreement with the increased absolute values of a* coordinates. / Filmes de nitreto de titânio com adição de nióbio ((TiN[Nb], 0,01 < Nb/Ti < 0,15) foram depositados pelo processo de pulverização catódica utilizando um sistema Triodo Magnetron Sputtering. A pulverização catódica de Titânio e Nióbio foi feita a partir de um alvo de titânio com insertos de nióbio dispostos na região de erosão. Foram analisados os efeitos da razão Nb/Ti na morfologia superficial do filme através de microscopia de força atômica e confocal. As medidas de refletividade dos filmes de TiN[Nb] obedecem perfeitamente o modelo de Drude-Lorentz. As constantes obtidas pelo modelo de Drude-Lorentz mostram um aumento nos valores da frequência de plasma e tempo de relaxação com o aumento na razão Nb/Ti, indicando que a presença de nióbio aumenta o número de portadores de carga. Os parâmetros de cor segundo o sistema CIELab mostram um aumento nas coordenadas L*, a* e b*. A análise visual das amostras mostra uma tonalidade avermelhada, quando comparadas com o filme contendo somente TiN, em concordância com o aumento absoluto nas coordenadas a*.

Relativity is one of the most important and well tested theories and Lorentz invariance is one of its pillars. Lorentz invariance violation (LIV), however, has been discussed in several quantum gravity and high energy models. For this reason, it is crucial to test it. Several tests, both terrestrial and astrophysical, have been performed in the last years and provide limits on the violation. This work takes part in these efforts and discuss the possibility of testing LIV with ultra-high energy cosmic rays (UHECRs). The effects of LIV in their propagation and the resulting changes in the spectrum of UHECRs are obtained and compared to the experimental data from the Pierre Auger Observatory. An analytical calculation for the inelasticity in the laboratory frame with LIV of any a + b &rarr; c + d interaction is presented and used to obtain the phase space and the energy losses of the pion production for protons, the photodisintegration for nuclei and the pair production for photons with LIV. A parametrization for the threshold energy of the photodisintegration with LIV is also proposed. The main effect seen is a decrease in the phase space and a resulting decrease in the energy loss. These changes have been implemented in Monte Carlo propagation codes and the resulting spectra of protons, nuclei and photons on Earth have been obtained and fitted to the data from the Pierre Auger Observatory. It is shown that upper limits on the photon LIV coefficient can be derived from the upper limits on the photon flux from the Pierre Auger Observatory. / Relatividade é uma das mais importantes e bem testadas teorias e a invariância de Lorentz é um de seus pilares. A violação da invariância de Lorentz (VIL), todavia, tem sido discutida em diversos modelos de gravidade quântica e altas energias. Por tal motivo, é crucial testá-la. Diversos testes, tanto terrestres quanto astrofísicos, foram realizados nos últimos anos e fornecem limites na violação. Este trabalho se insere nesses esforços e discute a possibilidade de testar VIL com raios cósmicos de altíssima energia. Os efeitos da VIL em sua propagação e as consequentes mudanças no espectro de raios cósmicos de altíssima energia são obtidos e comparados com os dados experimentais do Observatório Pierre Auger. Um cálculo analítico para a inelasticidade no referencial do laboratório com VIL para qualquer interação da forma a + b &rarr; c + d é apresentado e usado para obter o espaço de fase e as perdas de energia para a produção de píons para prótons, a fotodesintegração para núcleos e a produção de pares para fótons com VIL. Uma parametrização para o limiar de energia da fotodesintegração com VIL também é proposta. O principal efeito observado é uma diminuição no espaço de fase e uma consequente diminuição nas perdas de energia. Tais mudanças foram implementadas em códigos de Monte Carlo para a propagação e os espectros resultantes para prótons, núcleos e fótons na Terra foram obtidos e ajustados aos dados do Observatório Pierre Auger. É mostrado que limites superiores nos coeficientes de VIL para o fóton podem ser deduzidos dos limites superiores para o fluxo de fótons do Observatório Pierre Auger.

Made available in DSpace on 2016-08-18T18:19:25Z (GMT). No. of bitstreams: 1 Josberg Silva Rodrigues.pdf: 647762 bytes, checksum: 76e44a5c4743594c8862ff4d8b22704c (MD5) Previous issue date: 2009-04-30 / FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO / In this work we study the effects of the spontaneous breaking of Lorentz symmetry on black body radiation phenomenon in the context of the Maxwell-Caroll-Field-Jackiw (MCFJ) model. The MCFJ model is the electromagnetic CPT-odd sector of the standard model extension and, it presents for a purely space-like background a positive-definite hamiltonian. Firstly, we study the Maxwell electrodynamics by analyzing its hamiltonian structure following the Dirac s procedure for constrained systems. Then, we calculate the partition function via the path integrals formalism and consequently we obtain its thermodynamic properties such as: energy density, radiation pressure and the entropy. Afterwards, we apply the same procedure to find the partition function of the MCFJ model and we observe how the spectrum of black body changes due to the breaking of the CPT and Lorentz symmetries. We show that if the cosmic microwave background (CMB) radiation is described by this model, it shows an angular anisotropy in the energy density distribution. We also give, at leading order in the Lorentz violating parameter, the contributions of the Lorentz breaking for the Planck s radiation and the Stefan-Boltzmann laws. The Lorentz-violating (LV) corrections for the Planck s law is non-linear in the frequency and for the Stefan-Boltzmann law is quadratic in the temperature. Using our results, we set upper limits for the LV parameter by analyzing the Stefan-Boltmann law and the CMB anisotropy but it is shown that they are much less stringents that those obtained by birefringence or polarization analysis of light. / Esta dissertação aborda os efeitos da quebra espontânea da simetria de Lorentz sob a radiação do corpo negro no contexto da eletrodinâmica de Maxwell-Carroll-Field-Jackiw (MCFJ). O modelo MCFJ advém do setor CPT-ìmpar do modelo padrão estendido e apresenta uma hamiltoniana positiva-definida somente para um campo de fundo puramente tipo-espaço. O estudo começa pela eletrodinâmica de Maxwell realizando uma análise de sua estrutura hamiltoniana através do procedimento de Dirac para sistemas vinculados. Após essa análise, calcula-se a função de partição via o formalismo de integração funcional e obtendo consequentemente suas propriedades termodinâmicas relevantes como: densidade de energia, pressão de radiação e a entropia do sistema. Na segunda parte, seguindo um procedimento similar encontramos a função de partição do modelo MCFJ. Observa-se que o espectro de energia do corpo negro sofre alteração devido à quebra da invariância de Lorentz e da simetria CPT. Mostramos que se a radiação cósmica de fundo (RCF) for descrita por esse modelo desponta uma anisotropia na distribuição de densidade de energia. Também, mostramos que a lei de radiação de Planck e a lei de Stefan Boltzmann são afetadas pela introdução do campo externo responsável pela quebra de Lorentz. Tais modificações no caso da lei de Planck são não-lineares na frequência e na lei de Stefan-Boltzmann são quadráticas na temperatura. Usando esses resultados e os dados experimentais da constante de Stefan-Boltzmann e os dados referentes a anisotropia da radiação cósmica de fundo, estipulamos limites superiores para a magnitude do parâmetro da VL. Contudo, os limites obtidos são menos restritivos que os obtidos pela análise do fenômeno da birrefrigência.

Les sursauts gamma (GRBs pour "Gamma-Ray Bursts" en anglais) sont de brèves bouffées très énergétiques de rayonnement de haute énergie qui sont émises sur de courtes échelles de temps (fraction de seconde à plusieurs minutes). L'émission intense des sursauts gamma à haute énergie est supposée provenir d'un trou noir de masse stellaire nouvellement formé, accompagné d'un vent collimaté (i.e. un jet) se propageant à vitesse relativiste. L'émission est observée suivant deux phases successives, la phase prompte très erratique, et la phase de rémanence, moins lumineuse. Les deux instruments embarqués sur le satellite Fermi, le "Gamma-ray Burst Monitor" (GBM) et le "Large Area Telescope" (LAT), permettent d'étudier l'émission prompte des sursauts gamma sur une grande plage d'énergie (de ~10 keV à ~100 GeV). L'objectif principal de ma thèse est l'analyse et l'interprétation des propriétés spectrales et temporelles de l'émission prompte des GRBs observés par Fermi, en particulier avec les nouvelles données du LAT (Pass 8) qui ont été rendues publiques en juin 2015.La première partie de mon travail est une analyse spectrale résolue en temps de la phase prompte du sursaut GRB 090926A avec les données du GBM et du LAT. Mes résultats confirment avec un meilleur niveau de confiance la présence d'une cassure spectrale à ~400 MeV, qui est observée en coincidence avec un pic d'émission très court. Ils révèlent que cette atténuation spectrale est présente durant toute l'émission prompte du sursaut, et que l'énergie de cassure augmente jusqu'au GeV. L'interprétation de la cassure spectrale en termes d'absorption gamma ou de courbure naturelle du spectre d'émission Compton inverse (CI) dans le régime Klein-Nishina fournit des contraintes fortes sur le facteur de Lorentz du jet. Mes résultats conduisent en outre à des rayons d'émission R ∼10^14 cm qui sont compatibles avec une origine interne de l'émission du keV au GeV au-dessus de la photosphère du jet.La seconde partie de mon travail est une exploration du modèle de chocs internes développé par des collaborateurs à l'Institut d'Astrophysique de Paris (IAP). Ce modèle simule la dynamique du jet et les processus d'émission (synchrotron et CI) d'une population d'électrons accélérés aux chocs. J'ai simulé la réponse instrumentale de Fermi à un sursaut synthétique fourni par ce code numérique, et j'ai construit une fonction paramétrique qui peut être utilisée pour ajuster le modèle aux spectres de sursauts du keV au MeV. J'ai appliqué cette fonction avec succès à un échantillon de 64 sursauts brillants détectés par le GBM. J'ai aussi confronté le modèle de l'IAP au spectre d'émission prompte de GRB 090926A. Mes résultats montrent un bon accord, et j'ai identifié quelques pistes pour les améliorer. Les spectres synthétiques sont plus larges que tous les spectres dans l'échantillon du GBM. En conséquence, je discute brièvement quelques pistes de développements théoriques qui pourraient améliorer l'accord du modèle avec les observations, ainsi que des avancées observationnelles attendues dans le futur. / Gamma-Ray Bursts (GRBs) are very energetic and brief flashes of high-energy radiations which are emitted in a short time scale (fraction of a second to several minutes). The GRB bright emission is thought to be powered by a newly formed stellar-mass black hole that is accompanied by a collimated outflow (i.e. a jet) moving at a relativistic speed. The emission is observed as two successive phases: the highly variable “prompt” phase and the late and less luminous “afterglow” phase. The two instruments on board the Fermi space telescope, the Gamma-ray Burst Monitor (GBM) and the Large Area Telescope (LAT), allow the study of GRB prompt emission over a broad energy range (from ~10 keV to ~100 GeV). In June 2015, a new set of LAT data (Pass 8) was publicly released, which were generated using improved algorithms of reconstruction and classification of gamma-ray events. The main goal of my thesis is the analysis and interpretation of the spectral and temporal properties of the prompt emission phase of the GRBs observed by Fermi, especially using LAT Pass8 data.In the first part of my work, I performed a detailed time-resolved spectral analysis of the prompt phase of GRB 090926A with GBM and LAT data. My results confirm with a greater significance the spectral break at ∼400 MeV that is observed during a fast variability pulse, and they also reveal the presence of a spectral attenuation throughout the GRB prompt emission, as well as an increase of the break energy up to the GeV domain. I interpreted the spectral break in terms of gamma-ray absorption or as a natural curvature of the inverse Compton (IC) emission in the Klein-Nishina regime. Strong constraints on the jet Lorentz factor were obtained in both scenarios. My results lead also to emission radii R ∼10^14 cm, which are consistent with an internal origin of both the keV-MeV and GeV prompt emissions above the jet photosphere.The second part of my work is an exploration of the internal shock model that has been developed by collaborators at the "Institut d'Astrophysique de Paris" (IAP). This model simulates the GRB jet dynamics and the radiations (synchrotron and IC processes) from a population of shock-accelerated electrons. I simulated the response of the Fermi instruments to the synthetic GRB spectra provided by this numerical code. From these simulations, I built a new parametric function that can be used to fit the keV-MeV spectra of GRBs with the model. I applied successfully this function to a sample of 64 GBM bright GRBs. I confronted also the IAP model to the prompt emission spectrum of GRB 090926A. I obtained a relatively good agreement and I identified a couple of solutions that may improve it. The synthetic spectra are wider than any GRB spectra in the GBM sample. I present some theoretical developments that could improve the data-model agreement in the future, and I discuss possible advances from future GRB missions as well.