Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Física, Florianópolis, 2013. / Made available in DSpace on 2014-08-06T17:43:08Z (GMT). No. of bitstreams: 1 322925.pdf: 719239 bytes, checksum: 5f60bb1553822ecd79cff7e2d85e6605 (MD5) Previous issue date: 2013 / Nesta dissertação, elaboramos um estudo comparativo entre duas abordagens conceitualmente distintas da teoria efetiva de Euler-Kockel-Heisenberg. Na representação de interação para a eletrodinâmica quân- tica (QED), identificamos a contribuição para o espalhamento Halpern que, a baixas energias, leva à densidade lagrangiana efetiva correspondente. Posteriormente, no contexto da física de subtrações de Weisskopf, recuperamos este resultado, na representação de Heisenberg, através da variação da energia de ponto zero fermiônica causada pela presença de um campo eletromagnético externo. Para controlarmos as divergências no ultravioleta na densidade de energia do vácuo, utilizamos o método de regularização de Pauli-Villars-Rayski. Concluímos então que as duas abordagens são equivalentes no limite de baixas energias. <br> / Abstract : In this dissertation, we elaborate a comparative study between two conceptuallydistinct approaches to Euler-Heisenberg-Kockel effective theory.In the interaction Picture for quantum electrodynamics (QED), weidentify the contribution to Halpern scattering, which, at low energies,leads to the corresponding effective lagrangian density. In the sequence,we retrieve this result, in the Heisenberg Picture, through the variationin the fermion zero-point energy due to the presence of an externalelectromagnetic field. In order to circumvent the ultraviolet divergenciesin the vacum energy density, we employ the Pauli-Villars-Rayskiregularization method. We then conclude that the two approaches areequivalente in the low-energy limit.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2016. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2016-08-19T20:03:40Z No. of bitstreams: 1 2016_CarolineSilvaRochaCosta.pdf: 8897837 bytes, checksum: d30610cb36048450a15f18281ce44d61 (MD5) / Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2016-09-05T20:55:43Z (GMT) No. of bitstreams: 1 2016_CarolineSilvaRochaCosta.pdf: 8897837 bytes, checksum: d30610cb36048450a15f18281ce44d61 (MD5) / Made available in DSpace on 2016-09-05T20:55:43Z (GMT). No. of bitstreams: 1 2016_CarolineSilvaRochaCosta.pdf: 8897837 bytes, checksum: d30610cb36048450a15f18281ce44d61 (MD5) / Neste trabalho, analisamos o efeito Casimir para bósons e férmions em um hipertoros para ambos os casos à temperatura zero e à temperatura finita. Mostramos que, à temperatura zero, existe uma transição de valores negativos para valores positivos de pressão que dependem altamente dos parâmetros de compactificação. Com o implemento da temperatura, à baixas temperaturas, uma mudança na relação entre comportamento da pressão e os parâmetros de compactificação é observada, embora, para altas temperatura, devido à predominância do termo de radiação de corpo negro na pressão, essa mudança se torna irrelevante. Em seguida, utilizamos esses resultados para considerar um modelo não massivo e não interagente da Cromodinâmica Quântica e estimar a possível contribuição do efeito de Casimir para a temperatura crítica de deconfinamento dos quarks. _________________________________________________________________________________________________ ABSTRACT / In this work we analyse the Casimir effect for bosons and fermions on a hypertorus for both cases at zero and finite temperature. We find that at zero temperature there is a transition from negative to positive values of pressure which depends heavily on the magnitude of the compactification parameters. When low temperatures are considered, a change in the relation between the pressure behaviour and the compactification parameters is observed. In contrast, at high energies, due to the dominance of the black-body radiation term in the pressure, this change becomes insignificant. We then use these results to consider a non-interacting massless QCD model and estimate the possible contribution of the Casimir effect for the critical temperature of quarks deconfinement.

Let G be a Lie group acting on a homogeneous space G/K. The center of the universal enveloping algebra of the Lie algebra of G maps homomorphically into the center of the algebra of differential operators on G/K invariant under the action of G. In the case that G is a Jacobi Lie group of rank 2, we prove that this homomorphism is surjective and hence that the center of the invariant differential operator algebra is the image of the center of the universal enveloping algebra. This is an extension of work of Bringmann, Conley, and Richter in the rank 1case.

No description available.

Este trabalho é dedicado à investigação de diferentes aspectos da física de monocamadas de grafeno suspenso e epitaxial. A descrição do grafeno é baseada no modelo quase-relativístico de Dirac. Isso permite a aplicação dos métodos da Teoria Quântica de Campos (TQC) na investigação dos efeitos de interação entre o grafeno e o campo eletromagnético (EM). Usando o formalismo de integral de trajetória, nós formulamos uma teoria efetiva do campo EM na presença de monocamadas de grafeno. Esta teoria é governada pelo operador de polarização das quase-partículas de Dirac. Dois fenômenos importantes são investigados: as propriedades óticas do grafeno (o efeito Faraday em particular) e a interação de Casimir entre uma camada de grafeno e um metal paralelo. Em primeiro lugar, estudamos a propagação de ondas eletromagnéticas na presença de camadas de grafeno. A dinâmica de ondas é governada pelas equações modificadas de Maxwell obtidas a partir da teoria efetiva para o campo EM. Nós calculamos os coeficientes de reflexão e transmissão de luz polarizada linearmente e investigamos detalhadamente o efeito quântico de Faraday no campo magnético externo. Em particular, mostramos que as previsões do modelo de Dirac estão em boa concordância com os recentes resultados experimentais sobre a transmissão de luz e rotação de Faraday gigante em regime de ressonância cíclotron. Novos regimes também são previstos. Em segundo lugar, investigamos a interação de Casimir entre filmes suspensos de grafeno com um condutor ideal. O efeito é investigado tanto no caso ideal (temperatura nula, amostras ideais) quanto para configurações mais realistas (temperatura não nula e a presença de potencial químico). No caso de temperatura nula, a força de Casimir entre grafeno e condutor ideal é aproximadamente 2.6% da força entre dois condutores ideais. Ao mesmo tempo, no limite de temperatura elevada, o efeito mostra-se ser muito forte cerca de 50% de efeito entre metais ideais. / This research is devoted to investigation of several aspects of the physics of suspended and epitaxial graphene monolayers. The description of graphene is based on the quasi--relativistic Dirac model which permits application of the methods of the Quantum Field Theory to investigation of the interaction of graphene with electromagnetic field. Basing on the path integral formalism we formulate the effective theory for EM field in presence of graphene monolayers which is governed by the polarization operator of the Dirac quasi-particles in graphene. The two main phenomena in the interaction of graphene with electromagnetic field are studied: the optical properties of graphene (the Faraday rotation in particular), and Casimir interaction between graphene samples and parallel metal. First, we study the propagation of electromagnetic waves in presence of suspended and epitaxial graphene layers. Their dynamics is governed by the modified Maxwell equations obtained from the effective theory for EM field. We calculate the reflection and transmission coefficient for linearly polarized light and investigate in detail the quantum Faraday effect in external magnetic field. In particular it is showed that the prediction of the Dirac model are in good agreement with recent experimental results on transmission and giant Faraday rotation in cyclotron resonance. New regimes are also predicted Secondly, we investigate Casimir interaction between suspended graphene films with ideal conductor. The effect is investigated both in the idealistic case (zero temperature, ideal samples) and for realistic configurations (non zero temperature and/or presence of impurities and chemical potential). For zero temperature the Casimir force between graphene and a conductor is about 2.7% of that between two ideal conductors. At the same time in the high temperature limit the effect is showed to be greatly enhanced being about 50% of that between ideal metals.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-03Bitstream added on 2014-06-13T20:33:11Z : No. of bitstreams: 1 maia_cas_me_ift.pdf: 968895 bytes, checksum: 0a94d217b227cfdce0aee0d507acf35f (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Sabe-se já há algum tempo que a Teoria Quântica de Campos permite violações das Condições Clássicas de Energia na forma de densidades e fluxos de energia negativa. Um exemplo contundente é o efeito Casimir, onde o estado de vácuo do campo eletromagnético entre duas placas metálicas possui densidade de energia negativa. Porém, se as leis da física não colocassem restrições sobre tais violações das Condições de Energia, aparentemente seria possível usar energias negativas para, por exemplo, produzir violações macroscópicas da segunda lei da termodinâmica, da conjectura de cosmic censorship, além de se proporcionar a criação de wormholes e possíveis máquinas do tempo. Uma linha de pesquisa desenvolvida para abordar essa questão envolve as chamadas Desigualdades Quânticas, estudadas primeiramente por L.H. Ford, que são desigualdades sobre fluxos e densidades de energia negativa que impõem restrições capazes de tornar as violações acima não observáveis macroscopicamente. Nesta dissertação apresentaremos alguns exemplos de sistemas que possuem densidades ou fluxos de energia negativa, revisaremos os teoremas de Desigualdades Quânticas e discutiremos algumas de suas aplicações. Discutiremos também algumas limitações destes teoremas apresentando sistemas que não estão sujeitos a desigualdades quânticas, dos quais um exemplo é o próprio efeito Casimir. Iremos enfim propor um modelo que introduz flutuações quânticas nas condições de contorno (e.g., nas placas metálicas) do efeito Casimir, e iremos mostrar que a introdução destes efeitos de flutuação no cálculo da energia de Casimir tem por resultado impedir que violações de leis físicas macroscópicas manifeste-se nesse sistema. / Abstracts: It has been known for some time that Quantum Field Theory allows the violation of Classical Energy Conditions in the form of negative energy densities and fluxes. A remarkable exemple is the Casimir effect, where the vacuum state of the electromagnetic field between two perfectly conducting parallel plates presents negative energy density. However, if he laws of physics did not place constraints on such a violation of the Energy Conditions, it appears that it would be possible to use negative energies for producing, for example, macroscopic violation of the second law of thermodynamics, of the cosmic censorship conjecture, and also provide the creation of woemholes and time machines. A line of research wich was developed to approach this question is the so called Quantum Inequalities, first studied by L.H. Ford, which are constraints over negative energy densities and fluxes with capacity to render the above violations macroscopically unobservable. We present here some examples of systems with negative energy densities or fluxes, review the Quantum Inequalities theorems and discuss some of its applications. We also discuss some limitations of these theorems showing systems where there are no quantum inequalities, being the Casimir effect one example. At last we propose a model which introduces quantum fluctuations in the description of the boundaries conditions (e.g., the conducting plates) of Casimir effect and we'll show that the introduction of these fluctuations in the calculation of Casimir energy results in the impossibility of violation of macroscopic physical laws using Casimir configuration.

Este trabalho é dedicado à investigação de diferentes aspectos da física de monocamadas de grafeno suspenso e epitaxial. A descrição do grafeno é baseada no modelo quase-relativístico de Dirac. Isso permite a aplicação dos métodos da Teoria Quântica de Campos (TQC) na investigação dos efeitos de interação entre o grafeno e o campo eletromagnético (EM). Usando o formalismo de integral de trajetória, nós formulamos uma teoria efetiva do campo EM na presença de monocamadas de grafeno. Esta teoria é governada pelo operador de polarização das quase-partículas de Dirac. Dois fenômenos importantes são investigados: as propriedades óticas do grafeno (o efeito Faraday em particular) e a interação de Casimir entre uma camada de grafeno e um metal paralelo. Em primeiro lugar, estudamos a propagação de ondas eletromagnéticas na presença de camadas de grafeno. A dinâmica de ondas é governada pelas equações modificadas de Maxwell obtidas a partir da teoria efetiva para o campo EM. Nós calculamos os coeficientes de reflexão e transmissão de luz polarizada linearmente e investigamos detalhadamente o efeito quântico de Faraday no campo magnético externo. Em particular, mostramos que as previsões do modelo de Dirac estão em boa concordância com os recentes resultados experimentais sobre a transmissão de luz e rotação de Faraday gigante em regime de ressonância cíclotron. Novos regimes também são previstos. Em segundo lugar, investigamos a interação de Casimir entre filmes suspensos de grafeno com um condutor ideal. O efeito é investigado tanto no caso ideal (temperatura nula, amostras ideais) quanto para configurações mais realistas (temperatura não nula e a presença de potencial químico). No caso de temperatura nula, a força de Casimir entre grafeno e condutor ideal é aproximadamente 2.6% da força entre dois condutores ideais. Ao mesmo tempo, no limite de temperatura elevada, o efeito mostra-se ser muito forte cerca de 50% de efeito entre metais ideais. / This research is devoted to investigation of several aspects of the physics of suspended and epitaxial graphene monolayers. The description of graphene is based on the quasi--relativistic Dirac model which permits application of the methods of the Quantum Field Theory to investigation of the interaction of graphene with electromagnetic field. Basing on the path integral formalism we formulate the effective theory for EM field in presence of graphene monolayers which is governed by the polarization operator of the Dirac quasi-particles in graphene. The two main phenomena in the interaction of graphene with electromagnetic field are studied: the optical properties of graphene (the Faraday rotation in particular), and Casimir interaction between graphene samples and parallel metal. First, we study the propagation of electromagnetic waves in presence of suspended and epitaxial graphene layers. Their dynamics is governed by the modified Maxwell equations obtained from the effective theory for EM field. We calculate the reflection and transmission coefficient for linearly polarized light and investigate in detail the quantum Faraday effect in external magnetic field. In particular it is showed that the prediction of the Dirac model are in good agreement with recent experimental results on transmission and giant Faraday rotation in cyclotron resonance. New regimes are also predicted Secondly, we investigate Casimir interaction between suspended graphene films with ideal conductor. The effect is investigated both in the idealistic case (zero temperature, ideal samples) and for realistic configurations (non zero temperature and/or presence of impurities and chemical potential). For zero temperature the Casimir force between graphene and a conductor is about 2.7% of that between two ideal conductors. At the same time in the high temperature limit the effect is showed to be greatly enhanced being about 50% of that between ideal metals.

Ce mémoire présente la réalisation d'un dispositif expérimental de deuxième génération pour le projet FORCA-G (FORce de CAsimir et Gravitation à courte distance). L'objectif de ce projet est la mesure des interactions à faible distance entre un atome et une surface massive. La mesure de force est réalisée à l'aide d'interféromètres atomiques utilisant des atomes confinés dans un réseau optique 1D vertical basé sur le déplacement des atomes de puits en puits. La dégénérescence des niveaux d'énergies des atomes dans les puits du réseau est levée par la force que l'on cherche à mesurer. Des transitions Raman permettent de séparer les atomes dans des puits adjacents, puis de les recombiner, créant ainsi un interféromètre atomique qui permet de mesurer la différence d'énergie entre puits, liée à la fréquence de Bloch nu B du réseau. Ce travail présente la mise en place d'un dispositif proprement dédié au projet, qui permettra à terme de mesurer les forces à faible distance. Il rend compte des améliorations obtenues en configuration de gravimètre sur la sensibilité court terme de la mesure qui atteint 5. 10^-6 à 1 s. Il regroupe l'étude des limitations de la sensibilité, de l'exactitude et l'étude de la perte de contraste des interféromètres. Il présente aussi la mise en place d'une étape supplémentaire : l'implémentation d'un piège dipolaire visant obtenir un échantillon d'atomes plus dense et plus froid. / The thesis presents the set up of the second version of the experiment FORCA-G (CAsimir FORce and Gravitation at short range). The purpose of this experiment is the measurement of short-range interactions between an atom and a massive surface. The measurement is realised thanks to atom interferometers using atoms trapped in a 1D vertical optical lattice. The energy levels of atoms in such a trap are shifted from lattice site to another by the force we aim at measuring. We move the atoms from site to site using counter-propagating Raman transitions. The atoms are moved from Δm lattice sites only if the Raman frequency matches υHFS +∆m.υB where υHFS is the frequency of the hyperfine ground state transition and υB is the Bloch frequency and represents the difference of potential energy between two wells in the case where the atoms are far from the surface. This thesis presents the implementation of a setup properly dedicated to FORCA-G in which the measurement of short-range forces will be possible. It reaches an improved short-term relative sensitivity on the measurement of the Bloch frequency of at 3.9 10-6 at 1s. It contains the studies of the limits in the sensitivity, the accuracy and the contrast losses. It also presents the implementation of a dipolar trap to further cool the atoms and increase their density (crossed dipolar trap with a 1064 broadband laser).

Ce travail de thèse présente la modélisation théorique de l'expérience FORCA-G. L'objectif de cette expérience est la mesure des interactions à courte portée entre des atomes piégés dans un réseau optique et une surface massive à une grande précision. Nous nous sommes intéressés plus particulièrement à l'effet Casimir-Polder induit par la surface sur les atomes. Le but était de fournir la prédiction la plus précise possible des états atomiques. Ceci a consisté à considérer les effets de la température sur l'interaction Casimir-Polder et modéliser la surface de la manière la plus réaliste possible. Afin de résoudre le problème de divergence qu'impliquait un traitement perturbatif de l'interaction atome-surface, nous avons développé une méthode numérique pour un traitement non-perturbatif de l'interaction Casimir-Polder et modélisé l'interaction atome-surface à très courte distance par un potentiel de Lennard-Jones. Chaque effet et incertitude sur les états atomiques ont été évalués afin de déterminer s'ils seraient observables ou un facteur limitant en regard de la précision visée par l'expérience. Enfin nous nous sommes intéressés au cas d'un déséquilibre thermique entre la température du miroir et la température de l'environnement qui pourrait être induit par les lasers en présence ou un laser de chauffage. Nous avons calculé la correction du potentiel Casimir-Polder due au déséquilibre et évalué l'effet sur les niveaux d'énergie atomiques pour déterminer si cet effet pouvait être mesuré. / This thesis presents the theoretical modeling of the experiment FORCA-G. The purpose of this experiment is to measure short-range interactions between trapped atoms in an optical lattice and a massive surface with a high precision. We are focused on Casimir-Polder effect induced by the surface on the atoms. The aim was to give the most possible precise prediction of atomic states. This work took the temperature effects on Casimir-Polder interaction into account, modelled the surface of the experiment. In order to solve the divergence problem due to the perturbative treatment of the atom-surface interaction, we developed a digital method for a non-perturbative treatment of the Casimir-Polder interaction and modelled the short-range atom-surface interaction by a Lennard-Jones potential. Each effect and uncertainties on the atomic states were evaluated so that we know if they could be observable or a limiting factor compared to the experiment precision. Finally we were focused on an out of thermal equilibrium situation between the miroir and environment temperature which may be induced by the lasers. We computed the correction to the Casimir-Polder potential due to this disequilibrium and evaluated the effect on the atomic states.

The spectral theory of the Laplace operator has long been studied in connection with physics. It appears in the wave equation, the heat equation, Schroedinger's equation and in the expression of quantum effects such as the Casimir force. The Casimir effect can be studied in terms of spectral invariants computed entirely from the spectrum of the Laplace operator. It is these spectral invariants and their computation that are the object of study in the present work. The objective of this thesis is to present a computational framework for the spectral zeta function $\zeta(s)$ and its derivative on a Euclidean domain in $\mathbb{R}^2$, with rigorous theoretical error bounds when this domain is polygonal. To obtain error bounds that remain practical in applications an improvement to existing heat trace estimates is necessary. Our main result is an original estimate and proof of a heat trace estimate for polygons that improves the one of van den Berg and Srisatkunarajah, using finite propagation speed of the corresponding wave kernel. We then use this heat trace estimate to obtain a rigorous error bound for $\zeta(s)$ computations. We will provide numerous examples of our computational framework being used to calculate $\zeta(s)$ for a variety of situations involving a polygonal domain, including examples involving cutouts and extrusions that are interesting in applications. Our second result is the development a new eigenvalue solver for a planar polygonal domain using a partition of unity decomposition technique. Its advantages include multiple precision and ease of use, as well as reduced complexity compared to Finite Elemement Method. While we hoped that it would be able to contend with existing packages in terms of speed, our implementation was many times slower than MPSPack when dealing with the same problem (obtaining the first 5 digits of the principal eigenvalue of the regular unit hexagon). Finally, we present a collection of numerical examples where we compute the spectral determinant and Casimir energy of various polygonal domains. We also use our numerical tools to investigate extremal properties of these spectral invariants. For example, we consider a square with a small square cut out of the interior, which is allowed to rotate freely about its center.