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The motivation of this thesis is to look for a signature of Lorentz violation, hopefully observable, in the gravitational waves emitted by cosmic strings. Aspects of cosmic strings are reviewed, in particular how focused bursts of gravitational radiation are emitted when a cusp forms on the string. The same phenomenon is then studied in an effective field theory with Lorentz violation called Einstein-aether theory. This is a simple theory with a dynamic preferred frame, but it retains rotational and diffeomorphism invariance. The linearized version of the theory produces five wave modes. We study the usual transverse traceless modes which now have a wave speed that can be lower or greater than the speed of light. This altered speed produces distinctive features in the waves. They depend on two free parameters: roughly the wave speed and the acceleration of the string cusp. The profile of the wave is analyzed in detail for different values of the parameters and explained by close comparison with the string motion.

An introduction to periodic orbit techniques for deterministic dynamical systems is presented. The Farey map is considered as examples of intermittency in one-dimensional maps. The effect of intermittency on the Markov partition is considered. The Gauss map is shown to be related to the farey map by a simple transformation of trajectories. A method of calculating periodic orbits in the thermostated Lorentz gas is derived. This method relies on minimising the action from the Hamiltonian description of the Lorentz gas, as well as the construction of a generating partition of the phase space. This method is employed to examine a range of bifurcation processes in the Lorentz gas. A novel construction of the Sinai billiard is performed by using symmetry arguments to reduce two particles in a hard walled box to the square Sinai billiard. Infinite families of periodic orbits are found, even at the lowest order, due to the intermittency of the system. The contribution of these orbits is examined and found to be tractable at the lowest order. The number of orbits grows too quickly for consideration of any other terms in the periodic orbit expansion. A simple stochastic model for the diffusion in the Lorentz gas was constructed. The model produced a diffusion coefficient that was a remarkably good fit to more precise numerical calculations. This is a significant improvement to the Machta-Zwanzig approximation for the diffusion coefficient. We outline a general approach to constructing stochastic models of deterministic dynamical systems. This method should allow for calculations to be performed in more complicated systems.

[Truncated abstract] This thesis presents the design, construction and operation of a new rotating mod- ern Michelson-Morley test of Lorentz invariance. The experiment measures the isotropy of the speed of light by comparing the frequencies of two orthogonally ori- ented cryogenic sapphire whispering gallery mode resonators. Putative violations of Lorentz invariance will manifest as periodic variations in the difference frequency between the two resonators, related to the changing orientation of the experiment with respect to a preferred cosmological frame. Actively rotating the experiment is advantageous for three reasons. Firstly, by careful selection of the rotation frequency in the laboratory we are able to sample the isotropy of the speed of light at a rate that coincides with the optimal frequency instabilities of the oscillators (18 seconds). Secondly, the statistics of this exper- iment are improved with respect to non-rotating (stationary) experiments, which rely on the motion of the Earth to sample the isotropy of the speed of light. This results from integrating over more periods of rotation per unit of time, compared to the sidereal rotation experienced by stationary experiments. ... Many noise sources and systematic disturbances have been characterized and the operation of the experiment optimized. Two frequencies are generated at 10 GHz with 226 kHz separation, exhibiting a fractional frequency instability of less than 2x10-14 from 5 to 500 seconds. Furthermore, the work includes a detailed analysis of the experiment within the Standard Model Extension and Robertson, Mansouri and Sexl frameworks. The sensitivity of the experiment to violations of Lorentz invariance has been derived in each of these frameworks, for both short data set and the complete full year analysis. The data has been analysed using two separate data analysis techniques, which were optimised for noise present in the data. We have operated the experiment over the course of more than one year, collect- ing data more than 30 percent of the time. By analysing over 1 year of data we were able to set the first independent limits on 8 parameters in the photon sector of the Standard Model Extension as low as 10-16 for Ke- and 10-12 for Ko+ parameters, improving upon previous non-rotating experiments by up to an order of magnitude. We have also set new a new limit on the isotropy parameter PMM = 9.4(8.1)x10-11 of the Robertson, Mansouri and Sexl framework, which is a factor of 25 improvement.

Zugl.: Ilmenau, Techn. Univ., Diss., 2008

University, Diss., 2001--München.

Humboldt-Universiẗat, Diss., 2001--Berlin.

CAVALCANTE, Roberto Vinhaes Maluf. Oscilador de Dirac: Implicações da violação da simetria de Lorentz e da massa dependente da posição. 2008. 66 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2008. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-29T21:54:48Z No. of bitstreams: 1 2008_dis_rvmcavalcante.pdf: 357709 bytes, checksum: 0d971f3de848805e1c0b6c73e388ba53 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-29T21:55:22Z (GMT) No. of bitstreams: 1 2008_dis_rvmcavalcante.pdf: 357709 bytes, checksum: 0d971f3de848805e1c0b6c73e388ba53 (MD5) / Made available in DSpace on 2015-05-29T21:55:22Z (GMT). No. of bitstreams: 1 2008_dis_rvmcavalcante.pdf: 357709 bytes, checksum: 0d971f3de848805e1c0b6c73e388ba53 (MD5) Previous issue date: 2008 / In this work we study the Dirac Oscillator (DO) in a threefold way. In the first way, we study DO with Lorentz symmetry violation. This violation is implemented through vectorial and an axial terms. We realize a non-relativistic limit and we obtain that the background vector field does not modify the energy spectrum. However, in the case of the background axial field, a correction similar to the Zeeman effect shows up. As the second issue studied here, we report first studies on the Dirac oscillator with variable mass. We impose a constraint in the system in order to preserve a supersymmetric structure and hence to obtain a wave function solution. This condition allows us to find a particular functional form to the mass, which presents an interesting feature. Due to this feature, this model enhances twofold physical equivalence for the Dirac oscillator, namely, an interaction term between an anomalous magnetic moment of neutral fermions and a charged sphere, and the confinement of quarks. Also eigenfunctions and eigenenergy of the fundamental state of the system are obtained. Finally, in the third part of our work, we use the so called Foldy-Wouthuysen approach in order to treat the ordering problem of the kinetic energy operator in the low energy theory. The ordering problem appears in the Schroedinger theory when we consider mass depending on position, since due to the presence of two operators in the kinetic term, the Hamiltonian turns ambiguous. In that work, starting from a Dirac oscillator which mass depends on position, we use the Foldy-Wouthuysen transformation to achieve a non-relativistic anti-Hermitian Hamiltonian with no ordering problem. As a matter of completeness we add two appendix, namely, an appendix A in order to present the confluent hypergeometric equation and their relations with special functions, and an appendix B, where we review briefly the Supersymmetric Quantum Mechanics. / Neste trabalho estudamos o Oscilador de Dirac (OD) em três diferentes situações. Na primeira situação estudamos o OD com violação da simetria de Lorentz. Referida violação é implementada através de um termo vetorial e de um termo axial. Realizamos o limite não-relativístico e obtemos que o campo de background vetorial não modifica o espectro de energia do sistema. Contudo, no caso do campo de background axial, aparece uma correção similar ao efeito Zeeman. Na segunda questão discutida aqui, relatamos os primeiros estudos sobre o oscilador de Dirac com massa variável. Impomos um vínculo no sistema de modo a preservar a estrutura supersimétrica e obter a solução de função de onda. Esta condição nos permite encontrar uma forma funcional específica para a massa, a qual apresenta interessante característica. Devido a esse aspecto, esse modelo melhora duas conhecidas interpretações físicas do Oscilador de Dirac, ou seja, aquela onde o OD é visto como uma interação entre o momento magnético anômalo de férmions neutros e uma esfera carregada, e a interpretação como um modelo que descreve aproximadamente o confinamento de quarks. Por outro lado, as autofunções e a autoenergias do estado fundamental do sistema são também obtidas. Por fim, na terceira parte do trabalho, usamos a conhecida abordagem de Foldy-Wouthuysen para tratar o problema de ordenamento do operador de energia cinética na teoria de baixas energias. O problema de ordenamento aparece na teoria de Schroedinger quando consideramos massa dependendo da posição, uma vez que a presença de dois operadores no termo cinético torna ambíguo o Hamiltoniano. Neste trabalho, partindo do oscilador de Dirac, no qual a massa depende da posição, usamos a transformação de Foldy-Wouthuysen para obter um Hamiltoniano não-relativístico e anti-hermitiano, sem problemas de ordenamento. Com o intuito de auxilair a leitura do trabalho do ponto de vista técnico, acrescentamos dois apêndices. No apêndice A apresentamos as equações hipergeométricas confluentes e suas relações com diversas funções especiais. No apêndice B, revisamos brevemente os conceitos básicos da Supersimetria da Mecânica Quântica.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013. / Submitted by Alaíde Gonçalves dos Santos (alaide@unb.br) on 2014-03-25T11:46:09Z No. of bitstreams: 1 2013_DhiegoLoioladeAraujo.pdf: 300749 bytes, checksum: 88e56177211a24bab917702ee10a7a0a (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2014-06-06T14:11:39Z (GMT) No. of bitstreams: 1 2013_DhiegoLoioladeAraujo.pdf: 300749 bytes, checksum: 88e56177211a24bab917702ee10a7a0a (MD5) / Made available in DSpace on 2014-06-06T14:11:39Z (GMT). No. of bitstreams: 1 2013_DhiegoLoioladeAraujo.pdf: 300749 bytes, checksum: 88e56177211a24bab917702ee10a7a0a (MD5) / Neste trabalho, estudamos superfícies tipo-espaço imersas no espaço de Lorentz-Heisenberg tridimensional que possuem curvatura média constante nula, denominadas superfícies máximas. Mostramos que a aplicação de Gauss de tais superfícies é uma aplicação harmônica na esfera de Riemann trivial, C∪{∞}, munida com uma métrica conforme. Resolvemos o problema de Calabi-Bernstein mostrando a não existência de gráficos máximos inteiros no espaço de Lorentz-Heisenberg e perturbando a diferencial de Hopf, obtemos diferenciais quadráticas holomorfas em superfícies máximas neste espaço. Por fim, construímos uma correspondência entre superfícies de curvatura média constante não nula em R3 e superfícies máximas no espaço de Lorentz-Heisenberg. ______________________________________________________________________________________ ABSTRACT / In this paper, we study the spacelike surfaces with zero mean curvature immersed in the Lorentz-Heisenberg space, called maximal surfaces. We prove that de Gauss map of maximal surfaces are harmonic maps into the trivial Riemann sphere, C∪{∞}, endowed with a conformal metric. We solve the Calabi-Bernstein problem showing the nonexistence of entire maximal graphs in the Lorentz-Heisenberg space, and disturbing the Hopf differential, we obtain holomorphic quadratic differentials on the maximal surfaces. We build a correspondence between non-zero constant mean curvature surfaces in R3 and maximal surfaces in the Lorentz-Heisenberg space.

Special relativity (SR) determines the properties of synchrotron radiation, but the corresponding mechanisms are frequently misunderstood. Time dilation is often invoked among the causes, whereas its role would violate the principles of SR. Here it is shown that the correct explanation of the synchrotron radiation properties is provided by a combination of the Doppler shift, not dependent on time dilation effects, contrary to a common belief, and of the Lorentz transformation into the particle reference frame of the electromagnetic field of the emission-inducing device, also with no contribution from time dilation. Concluding, the reader is reminded that much, if not all, of our argument has been available since the inception of SR, a research discipline of its own standing.