No description available.

No description available.

Développé dans les années 50, le modèle de Skyrme est un modèle efficace à basse énergie qui tente de représenter les noyaux atomiques. Bien qu'intéressant, le modèle original rencontre deux problèmes majeurs : il prédit des énergies de liaison trop élevées pour les noyaux et il leur prête une structure cristalline qui n'est pas observée expérimentalement. Afin de régler ces problèmes, Adam, Sánchez-Guillén et Wereszczynski, en 2010, ont développé le modèle de Skyrme BPS en modifiant le lagrangien du modèle original. Toutefois, leur version ne permet pas de représenter des particules physiques. C'est pour cette raison que le modèle de Skyrme quasi-BPS fut développé par Bonenfant et Marleau en 2010. Le lagrangien du modèle de Skyrme quasi-BPS comprend les termes du modèle de Skyrme original en plus de ceux du modèle de Skyrme BPS, soit des termes d'ordre zéro, deux, quatre, et six en dérivée. En 2018, Bartolini, Bolognesi et Proto proposèrent une façon de générer le lagrangien du modèle de Skyrme quasi-BPS en se basant sur le modèle de Sakai-Sugimoto, qui est une extension holographique de la chromodynamique quantique. Nous tenterons, pour ce projet de recherche, d'utiliser leur méthode afin de générer des termes d'ordre supérieur en dérivée dans le lagrangien. Ainsi, nous souhaitons explorer le parallèle entre le modèle d'élasticité et le modèle de Skyrme proposé par Manton en 1987. / Developed in the 50s, the Skyrme model is a low energy effective model that aims to represent atomic nuclei. Although interesting, the original model bumps into two major problems : it predicts binding energies that are too high compared to experimental results and gives the nuclei crystalline structures that are not observed experimentally. To solve these problems, Adam, Sánchez-Guillén and Wereszczynski, in 2010, developed the BPS Skyrme model by modifying the original lagrangian. However, their version cannot represent real particles. In order to remedy this problem, the q-BPS Skyrme model was developed by Bonenfant and Marleau in 2010. Its lagrangian includes both the terms from the lagrangian of the original Skyrme model and the ones from the lagrangian of the BPS Skyrme model, that is, terms of order 0, 2, 4 and 6 in derivative. In 2018, Bartolini, Bolognesi and Proto proposed a way to generate the q-BPS Skyrme model lagrangian using the Sakai-Sugimoto model, which is a holographic extension of quantum chromodynamics. We will try, for this research project, to generalize their method in order to generate higher order terms in derivative in the q-BPS lagrangian. This way, we hope to explore the parallel between the elasticity theory and the Skyrme model described by Manton in 1987.

Développé dans les années 50, le modèle de Skyrme est un modèle efficace à basse énergie qui tente de représenter les noyaux atomiques. Bien qu'intéressant, le modèle original rencontre deux problèmes majeurs : il prédit des énergies de liaison trop élevées pour les noyaux et il leur prête une structure cristalline qui n'est pas observée expérimentalement. Afin de régler ces problèmes, Adam, Sánchez-Guillén et Wereszczynski, en 2010, ont développé le modèle de Skyrme BPS en modifiant le lagrangien du modèle original. Toutefois, leur version ne permet pas de représenter des particules physiques. C'est pour cette raison que le modèle de Skyrme quasi-BPS fut développé par Bonenfant et Marleau en 2010. Le lagrangien du modèle de Skyrme quasi-BPS comprend les termes du modèle de Skyrme original en plus de ceux du modèle de Skyrme BPS, soit des termes d'ordre zéro, deux, quatre, et six en dérivée. En 2018, Bartolini, Bolognesi et Proto proposèrent une façon de générer le lagrangien du modèle de Skyrme quasi-BPS en se basant sur le modèle de Sakai-Sugimoto, qui est une extension holographique de la chromodynamique quantique. Nous tenterons, pour ce projet de recherche, d'utiliser leur méthode afin de générer des termes d'ordre supérieur en dérivée dans le lagrangien. Ainsi, nous souhaitons explorer le parallèle entre le modèle d'élasticité et le modèle de Skyrme proposé par Manton en 1987. / Developed in the 50s, the Skyrme model is a low energy effective model that aims to represent atomic nuclei. Although interesting, the original model bumps into two major problems : it predicts binding energies that are too high compared to experimental results and gives the nuclei crystalline structures that are not observed experimentally. To solve these problems, Adam, Sánchez-Guillén and Wereszczynski, in 2010, developed the BPS Skyrme model by modifying the original lagrangian. However, their version cannot represent real particles. In order to remedy this problem, the q-BPS Skyrme model was developed by Bonenfant and Marleau in 2010. Its lagrangian includes both the terms from the lagrangian of the original Skyrme model and the ones from the lagrangian of the BPS Skyrme model, that is, terms of order 0, 2, 4 and 6 in derivative. In 2018, Bartolini, Bolognesi and Proto proposed a way to generate the q-BPS Skyrme model lagrangian using the Sakai-Sugimoto model, which is a holographic extension of quantum chromodynamics. We will try, for this research project, to generalize their method in order to generate higher order terms in derivative in the q-BPS lagrangian. This way, we hope to explore the parallel between the elasticity theory and the Skyrme model described by Manton in 1987.

A skyrmion is a vortex-like spin pattern which has been observed in so-called B20 magnetic systems such as MnSi, (Mn,Fe)Si and a few other metallic magnets as well as in insulating Cu₂OSeO₃. We conduct a comprehensive study of muon spin relaxation (μSR) on bulk single crystals of MnSi and (Mn,Fe)Si, a MBE thin film of MnSi, and a ceramic specimen of Cu₂OSeO₃ in this work. The generic second-order like phase transition indicated by 1/T₁ peaks at T_c in bulk systems is discussed in light of the Brazovskii-type first-order phase transition due to the presence of the DM interaction. We also discuss the different temperature dependences of μ⁺ spin-lattice relaxation rate 1/T₁ in bulk pure systems MnSi and Cu₂OSeO₃ and their commonalities in the paramagnetic state and the ordered state due to the DM interaction. Furthermore, we highlight the enhanced 1/T₁ in the skyrmion crystal (SkX) phase compared to neighboring conical phases due to an abundance of low-energy magnetic fluctuations/excitations. This abundance is corroborated by the reduced static order parameter in the SkX phase of MnSi compared to neighboring conical phases, deduced by combining μSR experiments and magnetic field simulations. The intermediate (IM) region above T_c, where the modification of magnetic transition by the DM interaction starts to appear in MnSi, exhibit multi-time scale spin fluctuations, topologically non-trivial Hall resistivity and non-Fermi-liquid exponent of longitudinal resistivity in single-crystal Mn₀.₉Fe₀.₁Si and the MnSi MBE thin film, similar to the magnetically disordered phase of pure MnSi under hydrostatic pressure. These three defining features indicate a fluctuating skyrmion liquid in this magnetically ordered state, stabilized by pressure, disorder or reduced dimensionality. Moreover, the magnetic transition is strongly first order in the MnSi MBE thin film sample, different from the Brazovskii-type weakly first order transition in bulk samples, suggesting the importance of reduced dimensionality in modifying the nature of magnetic phase transitions in B20 systems.

Neste trabalho estudamos aspecto estruturais de modelos onde os bárions são tratados como sólitons quirais, tais como o proposto pó Skyrme e variantes, contendo um termo estabilizador de sexta ordem, proporcional à corrente bariônica. Modelos deste tipo têm sido bastante estudados na literatura e suas predições para as propriedades estásticas do núcleon, sistematicamente, se mantêm por volta de 2/3 dos respectivos valores experimentais. Em geral, uma dada versão do modelo envolve apenas dois ou três parâmetros, mas pode dar origem a mais de uma dezena de previsões, e esta proliferação de números torna difícil a sua avaliação. Por isso, neste trabalho investigamos os vínculos estruturais ou numéricos entre as previsões do modelo, de modo a tornar mais objetiva a sua comparação com a experimentação. Todos os modelos considerados têm a mesma parte de longo alcance. Assim, a busca de padrões é feita considerando-se tanto versões diferentes das lagrangianas de curto alcance, vários valores para os parâmetros, e campos do píon que se transformam segundo representações não usuais de SU(2) X SU(2). Dessas várias possibilidades emerge um número muito grande de resultados numéricos que, depois de organizados, mostram regularidade. Dessas regularidades decorre uma proposta para a análise dos dados experimentais. Finalmente, este trabalho também inclui um cálculo alternativo do fator de forma píon-núcleon, a partir da interação NN do modelo de Skyrme. / In this work we study structural features of models where baryons are treated as chiral solitons, such as that proposed by Skyrme and variants, containing a sixth order stabilizing term, proportional to the baryonic current. Models of this kind have been widely considered in the literature and their predictions for nucleon static properties are systematically around 2/3 of the corresponding experimental values. In general a given version of the model contains only two or three parameters, but may hield more than ten observable predictions. This makes its assessment rather difficult. Therefore in this work we investigate structural and numerical constraints between the predictions of the model, so as to render the comparision with experimental more objective. All the models considered here contain the same long range parl. Hence the search of patterns is clone by considering different versions for the short range lagrangian. Various values for the free parameters and pion fields which transform according to unusual representations of SU(2) x SU(2) . A rather large amount of numerical results emerge form these various possibilities, which display regularities after being organized. These patterns motivate a proposal for the analysis of experimental information. Finally, this work also includes an altenative calculation for the pion-nucleon form factor, starting from the NN interaction in the Skyrme model.

La méthode dite de la fonctionnelle de la densité d'énergie (EDF) est l'outil théorique de référence pour l'étude systématique de la structure des noyaux atomiques de masse A>20. La méthode EDF est formulée en deux étapes successives consistant à briser puis à restaurer les symétries du Hamiltonien nucléaire sous-jacent. La technique de restauration des symétries n'est cependant rigoureusement formulée que si la fonctionnelle d'énergie dérive explicitement d'une interaction effective, i.e. d'un pseudo-potentiel, ce qui constitue un cas particulier de la méthode EDF plus générale. Ainsi, et comme cela a été démontré récemment, l'utilisation des paramétrisations existantes des fonctionnelles d'énergie conduit à l'obtention de résultats non physiques. Le pouvoir prédictif limité des fonctionnelles d'énergie existantes et leur inocuité relative à la restauration des symétries, nécessitent aujourd'hui de repenser leur méthode de construction. La première partie de ce travail a été dédié à l'analyse approfondie du problème associé à la restauration de symétrie et à l'identification de pistes permettant de contraindre la forme analytique des fonctionnelles d'énergie ne dérivant pas d'un pseudo-potentiel indépendant du système. La seconde partie a consisté à développer un pseudo-potentiel rendant la restauration des symétries automatiquement bien définie. Les difficultés de ce travail ont résidé dans (i) l'identification de la complexité minimale du pseudo-potentiel nécessaire à l'obtention d'une fonctionnelle d'énergie assez flexible pour égaler, et si possible améliorer, les performances des paramétrisations existantes, (ii) la dérivation analytique de la fonctionnelle et des champs à un corps découlant de celle ci, (iii) l'implémentation de ces derniers dans les codes de calculs, et dans (iv) le développement d'un protocole d'ajustement des paramètres adapté à la nouvelle fonctionnelle d'énergie ainsi développée. Les premiers résultats obtenus ont permis de valider l'approche en démontrant la flexibilité suffisante du pseudo-potentiel au niveau des calculs réalisés sans restauration des symétries. / The theoretical tool of choice for the microscopic description of all medium- and heavy-mass nuclei is the Energy Density Functional (EDF) method. Such a method relies on the concept of spontaneous symmetry breaking and restoration. In that sense, it is intrinsically a two-step approach. However, the symmetry restoration procedure is only well-defined in the particular case where the energy functional derives from a pseudo-potential. Thereby and as it has been recently shown, existing parameterizations of the energy functional provides unphysical results. Such a problem as well as the lack of predictive power call for developing new families of functionals. The first part of the present work is devoted to a study of the symmetry restoration problem and to the identification of properties that could constrain the analytic form of energy functionals that do not derive from a pseudo-potential. The second part deals with the construction of an energy functional that derives from a pseudo potential. The difficulties of such work are (i) the identification of the minimal complexity of the pseudo-potential necessary to obtain an energy functional that is flexible enough to provide high-quality EDF parameterizations, (ii) the tedious analytical derivation of the functional and of the associated one-body fields, (iii) the implementation of the latter in existing codes, and (iv) the development of an efficient fitting procedure. Eventually, it seems possible to generate a parameterization that strictly derives from a pseudo-potential and that provides as good results as state-of-the-art (quasi) bilinear functionals.

A interação forte a baixas energias pode ser abordada por meio de lagrangianas efetivas. Nesse contexto, o modelo de Skyrme representa uma forma de descrever bárions, que emergem como sólitons topológicos de uma lagrangiana mesônica quiral. A interação nucleon-nucleon (NN) é comumente tratada neste modelo de maneira aproximada, através do chamado Ansatz Produto (AP), cujo problema mais sério é não reproduzir a atração de alcance intermediário no canal escalar-isoescalar do potencial NN. O objetivo deste trabalho é construir um novo ansatz para o cálculo da interação NN no modelo de Skyrme. Para isso, analisamos o AP, investigando as causas deste problema fenomenológico, e concluímos que deve-se à componente azimutal de seu campo piônico. A partir disto, construímos o Ansatz Novo (AN), com o qual calculamos o novo potencial. Comparando os resultados com outros potenciais existentes, mostramos que o AN constitui uma solução plausível para o problema. / Strong interactions at low energies can be treated by means of effective lagrangians. In this context, the Skyrme model is regarded as a way to describe baryons as topological solitons from a chiral mesonic lagrangian. In the framework of this model, nucleon-nucleon (NN) interaction is usually derived in the sudden approximation, by means of the so called Product Ansatz (PA). Its most serious problem is the absence of the intermediate range attraction in the scalar-isoscalar channel of the NN potential. We construct a new ansatz to derive the NN interaction in the Skyrme model. At first, we analise the PA and investigate the causes of its phenomenological problem. We conclude it is due to the azimuthal component of its pionic field. With this result we build the New Ansatz (NA) and calculate the new potential. Comparisons of the results with other existent potentials show that NA constitutes a plausible solution to the problem.

Neste trabalho estudamos aspecto estruturais de modelos onde os bárions são tratados como sólitons quirais, tais como o proposto pó Skyrme e variantes, contendo um termo estabilizador de sexta ordem, proporcional à corrente bariônica. Modelos deste tipo têm sido bastante estudados na literatura e suas predições para as propriedades estásticas do núcleon, sistematicamente, se mantêm por volta de 2/3 dos respectivos valores experimentais. Em geral, uma dada versão do modelo envolve apenas dois ou três parâmetros, mas pode dar origem a mais de uma dezena de previsões, e esta proliferação de números torna difícil a sua avaliação. Por isso, neste trabalho investigamos os vínculos estruturais ou numéricos entre as previsões do modelo, de modo a tornar mais objetiva a sua comparação com a experimentação. Todos os modelos considerados têm a mesma parte de longo alcance. Assim, a busca de padrões é feita considerando-se tanto versões diferentes das lagrangianas de curto alcance, vários valores para os parâmetros, e campos do píon que se transformam segundo representações não usuais de SU(2) X SU(2). Dessas várias possibilidades emerge um número muito grande de resultados numéricos que, depois de organizados, mostram regularidade. Dessas regularidades decorre uma proposta para a análise dos dados experimentais. Finalmente, este trabalho também inclui um cálculo alternativo do fator de forma píon-núcleon, a partir da interação NN do modelo de Skyrme. / In this work we study structural features of models where baryons are treated as chiral solitons, such as that proposed by Skyrme and variants, containing a sixth order stabilizing term, proportional to the baryonic current. Models of this kind have been widely considered in the literature and their predictions for nucleon static properties are systematically around 2/3 of the corresponding experimental values. In general a given version of the model contains only two or three parameters, but may hield more than ten observable predictions. This makes its assessment rather difficult. Therefore in this work we investigate structural and numerical constraints between the predictions of the model, so as to render the comparision with experimental more objective. All the models considered here contain the same long range parl. Hence the search of patterns is clone by considering different versions for the short range lagrangian. Various values for the free parameters and pion fields which transform according to unusual representations of SU(2) x SU(2) . A rather large amount of numerical results emerge form these various possibilities, which display regularities after being organized. These patterns motivate a proposal for the analysis of experimental information. Finally, this work also includes an altenative calculation for the pion-nucleon form factor, starting from the NN interaction in the Skyrme model.

A interação forte a baixas energias pode ser abordada por meio de lagrangianas efetivas. Nesse contexto, o modelo de Skyrme representa uma forma de descrever bárions, que emergem como sólitons topológicos de uma lagrangiana mesônica quiral. A interação nucleon-nucleon (NN) é comumente tratada neste modelo de maneira aproximada, através do chamado Ansatz Produto (AP), cujo problema mais sério é não reproduzir a atração de alcance intermediário no canal escalar-isoescalar do potencial NN. O objetivo deste trabalho é construir um novo ansatz para o cálculo da interação NN no modelo de Skyrme. Para isso, analisamos o AP, investigando as causas deste problema fenomenológico, e concluímos que deve-se à componente azimutal de seu campo piônico. A partir disto, construímos o Ansatz Novo (AN), com o qual calculamos o novo potencial. Comparando os resultados com outros potenciais existentes, mostramos que o AN constitui uma solução plausível para o problema. / Strong interactions at low energies can be treated by means of effective lagrangians. In this context, the Skyrme model is regarded as a way to describe baryons as topological solitons from a chiral mesonic lagrangian. In the framework of this model, nucleon-nucleon (NN) interaction is usually derived in the sudden approximation, by means of the so called Product Ansatz (PA). Its most serious problem is the absence of the intermediate range attraction in the scalar-isoscalar channel of the NN potential. We construct a new ansatz to derive the NN interaction in the Skyrme model. At first, we analise the PA and investigate the causes of its phenomenological problem. We conclude it is due to the azimuthal component of its pionic field. With this result we build the New Ansatz (NA) and calculate the new potential. Comparisons of the results with other existent potentials show that NA constitutes a plausible solution to the problem.