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La théorie de cordes unifie de façon naturelle les théories de jauge, qui décrivent les interactions entre les particules élémentaires, avec une théorie quantique de la gravitation. Ces dernières années ont apporté de grands progrès dans la compréhension des états non-perturbatifs de la théorie, ses aspects holographiques, ainsi que la construction de modèles proches du Modèle Standard. Néanmoins, il reste des défis pour la théorie de cordes, qui incluent une définition non-perturbative, une meilleure compréhension de l'holographie, et le problème de la constante cosmologique. Ma recherche s'est concentrée sur des aspects formels des théories de gravitation quantique, qui incluent les trous noirs, la dépendance du temps, et l'holographie. Gr^ace à de nouveaux résultats dans le domaine de la théorie conforme avec spectre continu, mes collaborateurs et moi-m^eme avons avancé dans la compréhension de l'holographie dans des fonds avec dilaton linéaire, ainsi que dans le plongement de théories de jauge supersymétriques dans la théorie de cordes. En particulier, on a étudié des théories conformes supersymétriques avec spectre continu que l'on utilise pour construire des fonds de théories de cordes non-compacts et courbés. Les résultats obtenus nous ont permis de décrire des exemples explicites de symétrie miroir pour des fonds non-compacts. En introduisant des bords dans les théories conformes, on a analysé des états non-perturbatifs de la théorie de cordes, les D-branes. A basse énergie, les degrés de liberté sur les D-branes interagissent par des interactions de jauge. Avec ces outils, on a réussi à plonger une dualité infrarouge de théorie de jauge supersymétrique dans la théorie de cordes, et on a montré que la dualité correspond à une monodromie pour les états de bord dans l'espace de modules de la théorie conforme.<br><br> Dans cette thèse, on discute de nombreux autres liens entre la théorie conforme, la théorie de jauge et la gravitation. La plupart des contributions décrites étaient motivées par la théorie de cordes. Des exemples sont l'analyse d'états qui préservent la supersymétrie et leur lien avec les algèbres affines, la dépendance du temps et le dictionnaire holographique, l'analyse directe de la quantification de la gravité en présence d'un trou noir, la réalisation du scenario sans-bord pour la fonction d'onde de l'univers en théorie de cordes, une formule de Verlinde pour les théories conformes non-rationnelles et la construction de solutions non-géometriques à la supergravité. Dans d'autres travaux, je me suis concentré sur des théories qui quantifient la gravité plus directement, mais qui pourraient avoir moins de succès dans le problème de l'unification des forces en quatre dimensions. Ces théories ont quand-m^eme le potentiel de nous apprendre des aspects communs à toute théorie de gravitation quantique. Par exemple, on a analysé les degrés de liberté responsables de l'entropie d'un trou noir en trois dimensions, et nous avons argumenté sur la difficulté de reconcilier l'invariance modulaire avec l'unitarité en dehors de la théorie de cordes. On a aussi discuté la diffusion de ces trous noirs. D'autres contributions à la théorie de jauge non-commutative, la théorie de jauge supersymétrique, la production de paires dans un espace courbe, et cetera, sont aussi relativement indépendantes du cadre de la théorie de cordes.<br><br> Il me semble qu'il reste intéressant d'étudier des questions difficiles sur la théorie de jauge et la gravitation quantique, dans la cadre de la théorie de cordes, et en dehors de ce cadre, et d'^etre guidé par des problèmes ouverts durs qui doivent mener à un progrès concret par incréments ou par sauts.

Nonlinearities in quantum cascade lasers (QCL¡¯s) have wide applications in wavelength tunability and ultra-short pulse generation. In this thesis, optical nonlinearities in InGaAs/AlInAs-based mid-infrared (MIR) QCL¡¯s with quadruple resonant levels are investigated. Design optimization for the second-harmonic generation (SHG) of the device is presented. Performance characteristics associated with the third-order nonlinearities are also analyzed. The design optimization for SHG efficiency is obtained utilizing techniques from supersymmetric quantum mechanics (SUSYQM) with both material-dependent effective mass and band nonparabolicity. Current flow and power output of the structure are analyzed by self-consistently solving rate equations for the carriers and photons. Nonunity pumping efficiency from one period of the QCL to the next is taken into account by including all relevant electron-electron (e-e) and longitudinal (LO) phonon scattering mechanisms between the injector/collector and active regions. Two-photon absorption processes are analyzed for the resonant cascading triple levels designed for enhancing SHG. Both sequential and simultaneous two-photon absorption processes are included in the rate-equation model. The current output characteristics for both the original and optimized structures are analyzed and compared. Stronger resonant tunneling in the optimized structure is manifested by enhanced negative differential resistance. Current-dependent linear optical output power is derived based on the steady-state photon populations in the active region. The second-harmonic (SH) power is derived from the Maxwell equations with the phase mismatch included. Due to stronger coupling between lasing levels, the optimized structure has both higher linear and nonlinear output powers. Phase mismatch effects are significant for both structures leading to a substantial reduction of the linear-to-nonlinear conversion efficiency. The optimized structure can be fabricated through digitally grading the submonolayer alloys by molecular beam epitaxy (MBE). In addition to the second-order nonlinearity, performance characteristics brought by the third-order nonlinearities are also discussed, which include third-harmonic generation (THG) and intensity dependent (Kerr) refractive index. Linear to third-harmonic (TH) conversion efficiency is evaluated based on the phase-mismatched condition. The enhanced self-mode-locking (SML) effect over a typical three-level laser is predicted, which will stimulate further investigations of pulse duration shortening by structures with multiple harmonic levels.

We describe a procedure for classifying 4D N=2 superconformal theories of the type introduced by Davide Gaiotto. Any punctured curve, C, on which the 6D (2,0) SCFT is compactified, may be decomposed into 3-punctured spheres, connected by cylinders. The 4D theories, which arise, can be characterized by listing the ``matter" theories corresponding to 3-punctured spheres, the simple gauge group factors, corresponding to cylinders, and the rules for connecting these ingredients together. Different pants decompositions of C correspond to different S-duality frames for the same underlying family of 4D \mathcal{N}=2 SCFTs. We developed such a classification for the A_{N-1} and the D_N series of 6D (2,0) theories. We outline the procedure for general A_{N-1} and D_N, and construct, in detail, the classification through A_4 and D_4, respectively. / text

This work deals with the application of supermathematics to supersymmetrical problems arising in physics. Some recent developments are presented in detail. A reduction scheme for general supermanifolds to vector bundles is presented, which significantly simplifies their mathematical treatment in a physical context. Moreover, some applications of this new approach are worked out, such as the Fermi oscillator. / text

Exact solution of the Schr&ouml / dinger equation with some potentials is obtained. The normal and supersymmetric cases are considered. Deformed ring-shaped potential is solved in the parabolic and spherical coordinates. By taking appropriate values for the parameter q, similar results are obtained for Hulth&eacute / n and exponential type screened potentials. Similarly, Morse, P&ouml / schl-Teller and Hulth&eacute / n potentials are solved for the supersymmetric case. Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is also studied. The Nikiforov-Uvarov and Hamiltonian Hierarchy methods are used in the calculations. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. Results are in good agreement with ones obtained before.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-03Bitstream added on 2014-06-13T18:53:34Z : No. of bitstreams: 1 cardona_sah_me_ift.pdf: 677122 bytes, checksum: ef4eda2c094c5339bde81ff781b3d4cd (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A supersimetria é um tópico importante na física teórica atual. Em particular, tem-se dedicado grande esforço no estudo das extensões supersimétricas do Modelo Padrão (SM) desde a década de 80. A incorporação da supersimetria no SM resulta em uma grande quantidade de modelos. O modelo com o conteúdo mínimo de partículas assim como de interações é chamado o Modelo Mínimo Supersimétrico (MSSM). DEvido à supersimetria, todos os modelos supersimétricos apresentam diferenças com relação ao SM. A principal delas, além do conteúdo de partículas, está no setor de Higgs. Em particular, o setor de Higgs do modelo MSSM contem cinco graus de liberdade (cinco bósons de Higgs), diferentemente do SM, que contem apenas um bóson de Higgs. Outra diferença importante no caso do MSSM deve-se à mistura dos estados associados pela supersimetria aos bósons de Gauge e aos bósons de Higgs, chamados gauginos e higgsinos respectivamente, cujos autoestados de massa são conhecidos como charginos e neutralinos. Estas partículas desempenham um papel fundamental na possível descoberta da supersimetria na escala de energia de TeV's. / Supersymmetry is a fundamental topic in the actual theoretical physics. In particular, since the 80's, huge efforts have been done studying the supersymmetric extensions of the Standard Model (SM). Including supersymmetry in the SM generates a great amount of models. Among all of these, there is one that involves the minimum number of particles and interactions. This model is known as the Minimal Supersymmetric Standard Model (MSSM). Due to the incorporation of supersymmetry, all the extensions have differences in relation with the SM. The most remarkable one, beyond the particles content, lies in the Higgs sector. Particularly, in the MSSM Higg's sector there are five degrees of freedom (five Higgs bosons), in contrast with the SM (just one). Another difference is related wit the higgsino and gaugino mixture. This result in the presence of mass eigenstates known as charginos and neutralinos. The later particles play a fundamental role in the possible test of supersymmetry at the TeV's scales.

Made available in DSpace on 2016-08-18T18:19:30Z (GMT). No. of bitstreams: 1 Dissertacao Genilson.pdf: 3934400 bytes, checksum: f88bea8a3bd3a04623dda92abb3f6064 (MD5) Previous issue date: 2012-08-17 / FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO / We studied the localization of fermionic fields in a ring-like topological defect constructed with a real scalar field ϕ and immersed in (3, 1)−dimensional spacetime. The process of localization of fermions in the ring is analyzed by studying a Yukawa-like coupling ¯ ΨF(ϕ)Ψ, where F(ϕ) is a function of the real scalar field. Using the usual γ−matrices in (1, 1)−dimensions, we express the Dirac spinor in terms of its chiral left-handed and right-handed components. The amplitudes of fermions support Schr¨odinger-like equations allowing a probabilistic interpretation of them. In our case, to analyze the existence of resonances, we consider the coupling F(ϕ) = (1 − ϕ2)2. The eigenvalue equations are solved using numerical procedures. The eigenvalues that characterize the resonances are obtained for the two chiralities that show exactly the same, confirming the qualitative analysis of the potential are supersymmetric partners. / Estudamos a localização de campos fermiônicos num defeito topológico tipo anel construído com um campo escalar real ϕ e imerso no espaço-tempo de (3, 1)−dimensões. O processo de localização de férmions no anel é analisado estudando um acoplamento tipo Yukawa ¯ΨF(ϕ)Ψ, onde F(ϕ) é uma função do campo escalar real. Utilizando as matrizes−Γ usuais em (1, 1) dimensões, dividimos o espinor de Dirac em termos das duas componentes de quiralidade de mão-esquerda e mão-direita. As amplitudes dos f´ermions suportam equações tipo-Schrodinger possibilitando uma interpretação probabilística das mesmas. Em nosso caso específico, para analisarmos a existência de ressonâncias consideramos o acoplamento F(ϕ) = (1 − ϕ2)2. As equações de autovalores são solucionadas usando procedimentos numéricos. Os autovalores que caracterizam as ressonâncias são obtidas para as duas quiralidades que se mostram exatamente iguais confirmando a análise qualitativa dos potenciais serem parceiros supersimétricos.

Relations between propagators and Green<p>functions of Hamiltonians which are SUSY partners have been obtained. New exact propagators for the family of multi-well, time-dependent and non-hermitian potentials have been calculated.<p><p>Non-conservative SUSY transformation has been studied in<p>the case of multichannel Schrodinger equation with different thresholds. Spectrum (bound/virtual states and resonances) of the<p>non-conservative SUSY partner of zero potential has been founded. <p><p>Exactly solvable model of the magnetic induced Feshbach resonance<p>has been constructed. This model was tested in the case of Rb$^{85}$.<p><p>Conservative SUSY transformations of the first and the second order have been studied in the case of multichannel Schrodinger equation with equal thresholds. Transformations which introduce non-trivial coupling between scattering channels have been founded. <p><p>The first order SUSY transformation which preserves $S$-matrix eigen-phase shifts and<p>modifies mixing parameter has been founded in the case of two channel scattering with partial waves of different parities. In the case of coinciding parities we have found the second order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter. <p><p>Phenomenological two channel $^3S_1-^3D_1$<p>neutron-proton potential has been obtained by using single channel, phase equivalent and coupling SUSY transformations applied to zero potential. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

We describe a reproduction procedure which, given a solution of the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population. <br>To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions. <br><br>We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.<br><br>We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k).<br><br>The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n) <br>and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results.<br><br>We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)).<br>To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.<br>