General relativity is the successful classical theory describing gravitational interactions from cosmological scales down to the sub-millimetre scale. It has remained an open challenge to combine the principles of general relativity with those of the quantum world. A promising avenue has been put forward by Steven Weinberg, known as the asymptotic safety conjecture for gravity. It stipulates that a quantum field theory of gravity may very well exist as a fundamental and predictive theory up to highest energies. The central ingredient of this scenario is the existence of an interacting ultraviolet fixed point under the renormalisation group running of gravitational couplings. In this thesis, we study several aspects of asymptotic safety for gravity. Firstly, we offer a detailed qualitative and quantitative analysis of modern renormalisation group equations for Einstein-Hilbert gravity by contrasting different implementations of a Wilsonian momentum cutoff in combination with either heat kernel techniques or spectral sums. Secondly, we analyse in some depth the scale-dependence of gravitational couplings in the low-energy regime of Einstein-Hilbert gravity, where indications for the existence of an interacting infrared fixed point are found. Finally, we extend our analysis of renormalisation group trajectories to f(R)-type theories of gravity, and investigate how an interacting UV fixed point is connected with the classical low-energy regime. Implications of our findings are discussed.

We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.

The many-electron Schrödinger equation for atoms and molecules still remains analytically insoluble after over 90 years of investigation. This has not deterred scientists from developing a large variety of elegant techniques and approximations to workaround this issue and make many-particle quantum calculations computationally tractable. This thesis presents an all-particle treatment of three-particle systems which represent the simplest, most complex, many-particle systems including electron correlation and nuclear motion effects; meaning they provide a close-up view of fundamental particle interaction. Fully-Correlated (FC) energies and wavefunctions are calculated to high accuracy (mJ mol−1 or better for energies); and the central theme of this work is to use the wavefunctions to study fundamental quantum chemical physics. Nuclear motion has not received the same attention as electronic structure theory and this complicated coupling of electron and nuclear motions is studied in this work with the use of intracule and centre of mass particle densities where it is found nuclear motion exhibits strong correlation. A highly accurate Hartree-Fock implementation is presented which uses a Laguerre polynomial basis set. This method is used to accurately calculate electron correlation energies using the Löwdin definition and Coulomb holes by comparing with our FC data. Additionally the critical nuclear charge to bind two electrons within the HF methodology is calculated. A modification to Pekeris' series solution method is implemented to accurately model excited states of three-particle systems, and adapted to include the effects of nuclear motion along with three Non-Linear variational Parameters (NLPs) to aid convergence. This implementation is shown to produce high accuracy results for singlet and triplet atomic excited S states and the critical nuclear charge to bind two electrons in both spin states is investigated. Geometrical properties of three-particle systems are studied using a variety of particle densities and by determining the bound state stability at the lowest continuum threshold as a function of mass. This enables us to better ascertain what is meant when we define a system as an atom or a molecule.

The Super-K experiment determined that neutrinos are massive particles by observing the oscillation of atmospheric neutrinos. The SNO experiment confirmed this measurement by observing neutrinos from the Sun. The SNO+ experiment is intended to study the nature of neutrino masses by replacing the heavy water used in SNO with scintillator. The main goal of the experiment is to search for neutrinoless double-beta decay within 130Te. The SNO+ detector is much more sensitive to radioactive contamination than the SNO experiment. For this reason an external LED calibration system has been developed so the detector can be calibrated without risking contamination of the scintillator volume. This thesis describes the commissioning of this calibration system and its performance during the water phase of SNO+. The scintillator volume is separated from the surrounding detector via an acrylic vessel. As scintillator is less dense than water the position of the vessel is expected to shift throughout the lifetime of SNO+. A method to determine the position of the vessel using the external LED system is detailed as well as its performance. A measurement of the scattering length of the water surrounding the acrylic vessel using the same LED system is also presented. Calibration of the detector will also be performed using sources deployed within the vessel, and a study on the angular distribution of light from these sources and the effect of hardware upgrades is also presented. During the lifetime of the SNO+ experiment, the detector will be sensitive to neutrinos emitted from a supernovae within the Milky Way. A software framework was developed to accurately simulate the main interaction channels for supernova neutrinos within SNO+. The software was used to determine the burst trigger effciency during the water phase as well as a procedure to follow in the case of the burst. One outstanding problem in the field of neutrino physics is the neutrino mass hierarchy; whether there are two heavy and one light or two light and one heavy neutrino mass eigenstates. Neutrinos from a supernova burst may be able to solve this problem. A simple study is performed to determine the sensitivity of various detectors. The same analysis is performed using the aforementioned software to explore any systematic effects which may alter the sensitivity.

Trapped ions within Paul traps have shown to be a promising architecture in the realisation of a quantum information processor together with the ability of providing quantum simulations. Linear Paul traps have demonstrated long coherence times with ions being well isolated from the environment, single and multi-qubit gates and the high fidelity detection of states. The scalability to large number of qubits, incorporating all the previous achievements requires an array of linear ion traps. Microfabrication techniques allow for fabrication and micron level accuracy of the trap electrode dimensions through photolithography techniques. The first part of this thesis presents the experiential setup and trapping of Yb+ ions needed to test large ion trap arrays. This include vacuum systems that can host advanced symmetric and asymmetric ion traps with up to 90 static voltage control electrodes. Demonstration of a single trapped Yb+ ion within a two-layer macroscopic ion trap is presented. with an ion-electrode distance of 310(10) μm. The anomalous heating rate and spectral noise density of the trap was measured, a main form of decoherence within ion traps. The second half of this thesis presents the design and fabrication of multi-layer asymmetric ion traps. This allows for isolated electrodes that cannot be accessed via surface pathways, allowing for higher density of electrodes as well as creating novel trap designs that allow for the potential of quantum simulations to be demonstrated. These include two-dimensional lattices and ring trap designs in which the isolated electrodes provide more control in the ion position. For the microfabrication of these traps I present a novel high-aspect ratio electroplated electrode design that provides shielding of the dielectric layer. This provides a means to mitigate stray electric field due to charge build up on the dielectric surfaces. Electrical testing of the trap structures was performed to test bulk breakdown and surface flashover of the ion trap architectures. Results showed sufficient isolation between electrodes for both radio frequency and static breakdown. Surface flashover voltage measurements over the dielectric layer showed an improvement of more than double over previous results using a new fabrication technique. This will allow for more powerful ion trap chips needed for the next generation of microfabricated ion trap arrays for scalable quantum technologies.

In this thesis we study exact general relativistic space-times generated by a black hole and an additional source of gravity, while restricting to two classes of static and axially symmetric solutions: the Majumdar-Papapetrou solution for a couple (in general, a multiple system) of extremally charged black holes and the "superposition" of a Schwarzschild black hole with the Bach-Weyl thin ring. We follow the effect of the additional source on the geometry of black-hole space-time on the behaviour of important invariants, in particular of the simplest scalars obtained from the Riemann and possibly also Ricci tensor. We have plotted the invariants both outside and inside the black hole; in the case of a Schwarzschild black hole with ring, we found, to this end, an extension of the metric below the horizon. It turns out that the external source may affect the geometry inside the black hole considerably, even in the vicinity of singularity, although the singularity itself remains point-like in both solutions studied here.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-04-15T12:30:25Z No. of bitstreams: 1 PDF - Alessandra Uchôa.pdf: 1564895 bytes, checksum: 61bc9f483c207af02ed046e81c22e85d (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:20:29Z (GMT) No. of bitstreams: 1 PDF - Alessandra Uchôa.pdf: 1564895 bytes, checksum: 61bc9f483c207af02ed046e81c22e85d (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:20:37Z (GMT) No. of bitstreams: 1 PDF - Alessandra Uchôa.pdf: 1564895 bytes, checksum: 61bc9f483c207af02ed046e81c22e85d (MD5) / Made available in DSpace on 2016-07-22T20:20:37Z (GMT). No. of bitstreams: 1 PDF - Alessandra Uchôa.pdf: 1564895 bytes, checksum: 61bc9f483c207af02ed046e81c22e85d (MD5) Previous issue date: 2013-11-05 / The relevance of teaching about science has been an important issue for educational researches over the last decades. In this new approach, the use of history and philosophy of science is a promising pedagogical strategy to introduce them to treat about development of scientific knowledge in the context of education. To support our research, we in Martins (1990, 2006), Matthews (1995), El-Hani (2006), elements to understand the purpose of the study of the History of Science and justify its use in teaching science. In view of the insertion of the history of modern physics course in teacher training, was drafted six texts to be applied for future physics teachers. The student’s texts include major historical events from Aristotle to Einstein. With this material we intend to demystify the current view that the claims of the theory of special relativity is attributed only to Albert Einstein, without considering, or even decrease, the contribution of Poincaré, Lorentz and others that were of fundamental importance. / A relevância de ensinar conteúdos sobre as ciências tem se intensificado nas pesquisas educacionais das últimas décadas. Nesse sentido, a história e filosofia da ciência podem ser configuradas como sendo um interessante recurso pedagógico para tratar sobre a construção do conhecimento científico no ensino. Para subsidiar a nossa pesquisa, buscamos em Martins (1990; 2006), Matthews (1995), El-Hani (2006), elementos para entender o propósito dos estudos da História da Ciência, bem como justificar o seu uso no ensino da mesma. Na perspectiva da inserção da história da física moderna e contemporânea no curso de formação de professores, foi elaborado seis textos para ser aplicados para futuros professores de física. Os textos dos alunos contemplam os principais fatos históricos desde Aristóteles até Albert Einstein. Com este material pretendemos desmistificar a visão atual em que os créditos da teoria da relatividade especial são atribuídos somente a Albert Einstein, sem considerar, ou até mesmo diminuir, a contribuição de Poincaré, Lorentz e outros que foram de fundamental importância.

Neste trabalho, estudamos as subvariedades das formas espaciais pseudo-Riemannianas M^n_v(c) com vetor curvatura média de tipo luz, chamadas marginalmente aprisionadas, explorando as relações desta condição (motivada pela Física) com várias outras hipóteses de caráter geométrico, como lambda-isotropia, presença de nulidade relativa e invariância por um certo grupo de transformações de Lorentz. Em particular, apresentamos vários resultados de classificação e rigidez de superfícies marginalmente aprisionadas nos espaços de Lorentz-Minkowski L^4, de Sitter S^4_1 e anti-de Sitter H^4_1 nestes contextos, adaptando e generalizando resultados de alguns artigos. / In this work, we study the submanifolds of pseudo-Riemannian space forms M^n_v(c) with lightlike mean curvature vector, called marginally trapped, exploring the relations of this condition (motivated by Physics) with several other assumptions of geometric character, such as \\lambda-isotropy, presence of relative nullity and invariance by a certain group of Lorentz transformations. In particular, we prove several ridigity and classification results for marginally trapped surfaces in Lorentz-Minkowski space L^4, de Sitter space S^4_1 and anti-de Sitter space H^4_1 in these settings, adapting and generalizing results from several papers.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-23T11:33:13Z No. of bitstreams: 2 Dissertação - Calebe Martes de Andrade Santos - 2018.pdf: 2128372 bytes, checksum: a62b4d3a7f4bde06e5c3597ed5be80a4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-03-23T14:50:09Z (GMT) No. of bitstreams: 2 Dissertação - Calebe Martes de Andrade Santos - 2018.pdf: 2128372 bytes, checksum: a62b4d3a7f4bde06e5c3597ed5be80a4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-23T14:50:09Z (GMT). No. of bitstreams: 2 Dissertação - Calebe Martes de Andrade Santos - 2018.pdf: 2128372 bytes, checksum: a62b4d3a7f4bde06e5c3597ed5be80a4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-23 / This work has as main objective, besides exposing some techniques of solving differential equations of first and second order, to find solutions to Einstein Field Equation, through these techniques. The work was divided in 3 parts, being them, introduction and two other chapters. In the introduction, we tell a bit about the history of differential equations, as well as covering some important passages in the history of General Theory of Relativity. In the first chapter, in a preliminary way, a study was made on some differential equations of first and second orders. The second chapter refers to the application of second-order differential equations as a solution to Einstein's Field Equation. In this last chapter, we have done a study on the article Invariant solutions for the static vacuum equation and we present some other solutions to Einstein's Field Equation. For the writing of the work, a bibliographical revision was made in relation to the subjects addressed in it, thus relating the ideas and definitions of some authors throughout the text. / Este trabalho tem como principal objetivo, além de expôr algumas técnicas de resolução de equações diferenciais de primeira e segunda ordens, encontrar soluções para Equação de Campo de Einstein, através dessas técnicas. O trabalho foi dividido em 3 partes, sendo elas, introdução e mais dois capítulos. Na introdução, contamos um pouco da história das equações diferenciais, além de abordarmos alguns trechos importantes da história da Teoria da relatividade geral. No primeiro capítulo, de forma preliminar, foi feito um estudo sobre algumas equações diferenciais de primeira e segunda ordens. O segundo capítulo, refere-se à aplicação de equações diferenciais de segunda ordem como solução para Equação de Campo de Einstein. Neste último capítulo, fizemos um estudo sobre o artigo Invariant solutions for the static vacuum equation e expomos algumas outras soluções para Equação de Campo de Einstein. Para a escrita do trabalho, foi feita uma revisão bibliográfica em relação aos assuntos abordados no mesmo, relacionando assim, as ideias e definições de alguns autores no decorrer do texto.

Neste trabalho nós propomos uma estratégia Euclidiana para entender o efeito Unruh. Com este objetivo, nós inicialmente o estudamos para campos livres escalares sem massa, numa forma que é normalmente apresentada aos físicos e que é mais próxima ao trabalho original de Unruh I321| . Logo em seguida, deduzimos o efeito de um ponto de vista algébrico. Com este objetivo, estudamos as propriedades e as definições de estados KMS para compreender como um estado de equilíbrio é descrito na abordagem algébrica. Apresentamos os axiomas de Wightman para campos escalares assim como os de Osterwalder-Schrader. Usamos, então, o Teorema de Bisognano-Wichmann para estes campos e concluímos, baseados no trabalho de Sewell [27], que um observador uniformemente acelerado vê o estado de vácuo dos observadores inerciais como um estado KMS, e portanto, como um estado de equilíbrio. Novamente, concluímos a existência do efeito Unruh. Finalmente estudamos algumas relações entre probabilidade e análise funcional. Este estudo é fundamental para o entendimento do trabalho de Klein e Landau [15] e de Gérard e Jakel [7]. Estes trabalhos afirmam que existe uma relação biunívoca entre certos estados KMS e certos processos estocásticos (Klein e Landau) e uma relação entre certos processos estocásticos e espaços de trajetórias generalizados (Gérard e Jakel). Usando estes trabalhos e as funções de Schwinger para campos escalares, deduzimos o efeito Unruh de uma nova maneira. Acreditamos que este trabalho mostra um ponto de vista interessante do efeito Unruh e ilustra o uso do formalismo Euclidiano em teorias quânticas dos campos. Mesmo que algumas demonstrações para uma prova completa do efeito, usando técnicas Euclidianas, não são obtidas, devido às dificuldades técnicas encontradas, acreditamos que o material apresentado neste trabalho fornece, no mínimo, uma boa estratégia para a compreensão completa deste fenômeno físico. Além disto, as técnicas que são mostradas podem ser usadas em diversos problemas, como a construção de campos interagentes a uma temperatura finita, que permanecem atuais e promissores. / This paper proposes a Euclidean strategy to understand the Unruh effect. On that ground we first study it for free massless scalar fields the way it is usually presented to pliysicists, which is closer to Unruh\'s original work [32]. Then we infer the effect from an algebraic perspective. We study the proprieties and definitions of KklS states in order to understand the description of an equilibrium state in the algebraic approach. We present the Wightman\'s as well as Osterwalder-Schrader\'s axioms for scalar fields. Then we use the Bisognano-Wichmann theorem for these fields and conclude, based on Sewell work 1271, that a uniformly accelerated observer will observe tlie vacuum state of inertial observers as a KMS state and thus as an equilibrium state. Once again we infer the existence of the Cnruh effect. Finally we study some relations between probability and functional analysis. This study is crucial for understanding the work of Klein and Landau 1151 as well as of Gérard and Jakel (71. They state there is a biunivocal relation between certain KMS states and certain stochastic processes (Klein and Landau) and a relation between certain stochastic processes and generalized path spaces (Gérard and Jakel). Lsing these works and Schwinger functions for scalar fields, we deduce tlie Unruh effect in a new way. LVe believe this work shows an interesting aspect of the Unruh effect and represents the use of Euclidean formalism in quantum field theory. Although some demonstrations for a complete proof of the Unruh effect using Euclidean techniques were not obtained due to technical difficulties we faced, we believe the material presented in this paper provides at least a good strategy for the complete understanding of this physical phenomenon. Furthermore the techniques shown, which remain current and promising, can be used in different problems, sudy as the construction of interacting fields at a finite temperature.