Na teoria quântica é usual se referir a probabilidade de encontrar uma partícula entre as posições x e x + dx no instante t, embora a teoria não forneça quando ocorre a detecção. Nos primórdios da teoria, Pauli apresentou um argumento refutando a ideia de introduzir um operador que descreva a probabilidade do instante em que ocorre a detecção. Mais tarde, Page e Wootters, motivados pelo fato de não se observar autoestados de superposição de energia, apresentaram um formalismo quântico não-relativista num espaço estendido em que espaço e tempo desempenham papéis equivalentes, sendo consistente com as indagações feitas por Pauli. Isso leva a uma descrição dada pela probabilidade condicional de encontrar uma partícula entre x e x + dx em relação ao tempo [t, t + dt] dado por outra partícula, chamada de partícula relógio. Essa dissertação consiste de uma revisão da proposta de Page e Wootters para abordar o problema do tempo na mecânica quântica bem como de uma análise detalhada desta utilizando de ferramentas recentes introduzidas na área de informação quântica para o tratamento de simetrias em física. / In quantum theory it is usual one refers to the probability of finding a particle between the positions x and x + dx at time t, although the theory does not provide when detection occurs. In the primordies of the theory, Pauli presented an argument refuting the idea of introducing an operator describing the probability of the instant in which the detection occurs. Later, Page and Wootters, motivated by the fact that one is not able to observe energy eigenstates superposition, presented a non-relativistic quantum formalism in an extended space in which space and time play equivalent roles, being consistent with Pauli´s inquiries. This leads to a description given by the conditional probability of finding a particle between x and x + dx in respect to the time [t, t + dt] given by another particle, called the clock particle. This dissertation consists in a review of the Page and Wootters proposal to address the time problem in quantum mechanics as well as a detailed analysis of this using recent tools introduced in the area of quantum information for the treatment of symmetries in physics.

Lau Kai-Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract / Acknowledgements / Table of Contents / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-2 Method / Chapter 1.2 --- The G2 Method with Reduced M φller-Plesset Order and Basis Set / Chapter 1.3 --- The Gaussian-3 Method / Chapter 1.4 --- Our Modified G2 Methods / Chapter 1.5 --- Calculation of Thermodynamical Data / Chapter 1.6 --- Scope of the Thesis / Chapter 1.7 --- Remark on the Location of Transition Structures / Chapter 1.8 --- References / Chapter Chapter 2 --- A Gaussian-2 Study of the [C2H5O-] Potential Energy Surface and the Fragmentation Pathways of the Ethoxide Anion --- p.7 / Chapter 2.1 --- Introduction / Chapter 2.2 --- Theoretical Methods / Chapter 2.3 --- Results and Discussion / Chapter 2.3.1 --- Stable Isomers and TSs for the [C2H50-] Anions / Chapter 2.3.2 --- Fragmentation Pathways of the Ethoxide Anion (1-) / Chapter 2.4 --- Conclusions / Chapter 2.5 --- Publication Note / Chapter 2.6 --- References / Chapter Chapter 3 --- A Gaussian-2 Study of Isomeric C2H2N and C2H2N+ --- p.20 / Chapter 3.1 --- Introduction / Chapter 3.2 --- Theoretical Methods / Chapter 3.3 --- Results and Discussion / Chapter 3.3.1 --- The C2H2N and C2H2N+ Isomers / Chapter 3.3.2 --- The Cyanomethyl Radical (1) and Cation (1+) / Chapter 3.3.3 --- The Isocyanomethyl Radical (2) and Cation (2+) / Chapter 3.3.4 --- The lH-Azirinyl Radical (5) and Cation (5+) / Chapter 3.3.5 --- Other C2H2N and C2H2N+ Isomers / Chapter 3.3.6 --- The Unidentified C2H2N Isomer Formed in N + CH=CH2 / Chapter 3.4 --- Conclusions / Chapter 3.5 --- Publication Note / Chapter 3.6 --- References / Chapter Chapter 4 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Ethylene Oxide --- p.35 / Chapter 4.1 --- Introduction / Chapter 4.2 --- Theoretical Methods / Chapter 4.3 --- Results and Discussion / Chapter 4.3.1 --- Bond Cleavage Reactions / Chapter 4.3.2 --- Dissociation Channels Involving Transition Structure(s) / Chapter 4.4 --- Conclusions / Chapter 4.5 --- Publication Note / Chapter 4.6 --- References / Chapter Chapter 5 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Propylene Oxide --- p.47 / Chapter 5.1 --- Introduction / Chapter 5.2 --- Theoretical Methods / Chapter 5.3 --- Results and Discussion / Chapter 5.3.1 --- Bond Cleavage Reactions / Chapter 5.3.2 --- Dissociation Channels Involving Transition Structure(s) / Chapter 5.4 --- Conclusions / Chapter 5.5 --- Publication Note / Chapter 5.6 --- References / Chapter Chapter 6 --- A Gaussian-3 Study of the Thermochemistry of Chlorofluoromethanes (CFnCl4-n) and Their Cations (CFnCl4_n+)， n =0-4 --- p.61 / Chapter 6.1 --- Introduction / Chapter 6.2 --- Theoretical Methods / Chapter 6.3 --- Results and Discussions / Chapter 6.3.1 --- Heats of Formation of Chlorofluoromethanes and Their Cations / Chapter 6.3.2 --- Ionization Energies of Chlorofluoromethanes / Chapter 6.3.3 --- Proton Affinities of Chlorofluoromethanes / Chapter 6.4 --- Conclusions / Chapter 6.5 --- Publication Note / Chapter 6.6 --- References / Chapter Chapter 7 --- "A Gaussian-2 and Gaussian-3 Study of the Energetics and Structures of Cl2On and Cl2On+, n = 1，4, 6，and7" --- p.69 / Chapter 7.1 --- Introduction / Chapter 7.2 --- Theoretical Methods / Chapter 7.3 --- Results and Discussion / Chapter 7.3.1 --- Cl20 and Cl20+ / Chapter 7.3.2 --- Cl204 and Cl204+ / Chapter 7.3.3 --- Cl206 and Cl206+ / Chapter 7.3.4 --- Cl207 and Cl207+ / Chapter 7.4 --- Conclusions / Chapter 7.5 --- Publication Note / Chapter 7.6 --- References / Chapter Chapter 8 --- Conclusions --- p.81 / Chapter Appendix A --- The Gaussian-n (n = 1 - 3) Theoretical Models --- p.82 / Chapter A.1 --- The G1 and G2 theories / Chapter A.2 --- The G2(MP2) theory / Chapter A.3 --- "The G2(MP2,SVP) theory" / Chapter A.4 --- The G3 theory / Chapter Appendix B --- "Calculation of Enthalpy at 298 K, H298" --- p.86

Law Chi-Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.vi / List of Figures --- p.viii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1 / Chapter 1.2 --- The G3 Method with Reduced Mφller-Plesset Order and Basis Set --- p.2 / Chapter 1.3 --- The Gaussian-3X Method --- p.2 / Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.5 --- Remark on the Location of Equilibrium and Transition Structures --- p.3 / Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.5 / Chapter Chapter 2 --- Gaussian´ؤ3 Heats of Formation for (CH)6 Isomers --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Methods of Calculation and Results --- p.7 / Chapter 2.3 --- Discussion --- p.9 / Chapter 2.4 --- Conclusion --- p.11 / Chapter 2.5 --- Publication Note --- p.12 / Chapter 2.6 --- References --- p.12 / Chapter Chapter 3 --- A Gaussian-3 Investigation of N7 Isomers --- p.14 / Chapter 3.1 --- Introduction --- p.14 / Chapter 3.2 --- Computational Method and Results --- p.16 / Chapter 3.3 --- Discussion --- p.16 / Chapter 3.4 --- Conclusion --- p.24 / Chapter 3.5 --- Publication Note --- p.24 / Chapter 3.6 --- References --- p.24 / Chapter Chapter 4 --- A Gaussian-3 Study of N7+ and N7- Isomers --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Computational Method and Results --- p.29 / Chapter 4.3 --- Discussion --- p.30 / Chapter 4.3.1 --- The N7+ isomers --- p.30 / Chapter 4.3.2 --- The N7- isomers --- p.37 / Chapter 4.4 --- Conclusion --- p.41 / Chapter 4.5 --- Publication Note --- p.41 / Chapter 4.6 --- References --- p.41 / Chapter Chapter 5 --- "Thermochemistry of Chlorine Fluorides ClFn, n = 1-7, and Their Singly Charged Cations and Anions: A Gaussian-3 and Gaussian-3X Study" --- p.45 / Chapter 5.1 --- Introduction --- p.45 / Chapter 5.2 --- Methods of Calculations --- p.47 / Chapter 5.3 --- Results and Discussion --- p.48 / Chapter 5.3.1 --- Comparison of the G3 and G3X methods --- p.48 / Chapter 5.3.2 --- Assessments of the experimental results --- p.54 / Chapter 5.3.3 --- "Bond dissociation energies of ClFn, ClFn+, and ClFn-" --- p.57 / Chapter 5.3.4 --- Summary of the thermochemical data --- p.58 / Chapter 5.4 --- Conclusion --- p.59 / Chapter 5.5 --- Publication Note --- p.60 / Chapter 5.6 --- References --- p.60 / Chapter Chapter 6 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Dimethyl Sulfide --- p.63 / Chapter 6.1 --- Introduction --- p.63 / Chapter 6.2 --- Methods of Calculations --- p.64 / Chapter 6.3 --- Results and Discussion --- p.64 / Chapter 6.3.1 --- Bond cleavage reactions --- p.67 / Chapter 6.3.2 --- Dissociation channels involving transition structures --- p.68 / Chapter 6.4 --- Conclusion --- p.70 / Chapter 6.5 --- Publication Note --- p.70 / Chapter 6.6 --- References --- p.70 / Chapter Chapter 7 --- "Theoretical Study of the Electronic Structures of Carbon and Silicon Nanotubes, Carbon and Silicon Nanowires" --- p.72 / Chapter 7.1 --- Introduction --- p.72 / Chapter 7.2 --- Models and Computational Methods --- p.74 / Chapter 7.3 --- Results and Discussion --- p.75 / Chapter 7.4 --- Conclusion --- p.87 / Chapter 7.5 --- Publication Note --- p.87 / Chapter 7.6 --- References --- p.87 / Chapter Chapter 8 --- Conclusion --- p.90 / Appendix A --- p.91 / Appendix B

Cheng Mei-Fun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.vi / List of Figures --- p.viii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian-3 Method --- p.1 / Chapter 1.2 --- The G3 Method with Reduced Mφller-Plesset Order and Basis Set --- p.2 / Chapter 1.3 --- Density Functional Theory (DFT) --- p.3 / Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.5 --- Remark on the Location of Transition Structures --- p.3 / Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.5 / Chapter Chapter 2 --- Heats of Formation for the Azine Series: A Gaussian-3 Study --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Methods of Calculation and Results --- p.8 / Chapter 2.3 --- Discussion --- p.8 / Chapter 2.4 --- Conclusion --- p.9 / Chapter 2.5 --- Publication Note --- p.10 / Chapter 2.6 --- References --- p.10 / Chapter Chapter 3 --- Heats of Formation for Some Boron Hydrides: A Gaussian-3 Study --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Methods of Calculation and Results --- p.18 / Chapter 3.3 --- Discussion --- p.19 / Chapter 3.4 --- Conclusion --- p.21 / Chapter 3.5 --- Publication Note --- p.21 / Chapter 3.6 --- References --- p.21 / Chapter Chapter 4 --- Structural and Energetics Studies of Tri- and Tetra-tert-butylmethane --- p.30 / Chapter 4.1 --- Introduction --- p.30 / Chapter 4.2 --- Methods of Calculation and Results --- p.32 / Chapter 4.3 --- Discussion --- p.34 / Chapter 4.3.1 --- Mono-tert-butylmethane --- p.34 / Chapter 4.3.2 --- Di-tert-butylmethane --- p.35 / Chapter 4.3.3 --- Tri-tert-butylmethane --- p.37 / Chapter 4.3.4 --- Tetra-tert-butylmethane --- p.38 / Chapter 4.4 --- Conclusion --- p.39 / Chapter 4.5 --- Publication Note --- p.40 / Chapter 4.6 --- References --- p.40 / Chapter Chapter 5 --- A Computational Study of the Diels-Alder Reactions Involving Acenes: Reactivity and Aromaticity --- p.49 / Chapter 5.1 --- Introduction --- p.49 / Chapter 5.2 --- Methods of Calculation and Results --- p.50 / Chapter 5.3 --- Discussion --- p.51 / Chapter 5.4 --- Conclusion --- p.53 / Chapter 5.5 --- Publication Note --- p.53 / Chapter 5.6 --- References --- p.53 / Chapter Chapter 6 --- A Computational Study of the Charge- Delocalized and Charge-Localized Forms of the Croconate and Rhodizonate Dianions --- p.65 / Chapter 6.1 --- Introduction --- p.65 / Chapter 6.2 --- Methods of Calculation and Results --- p.67 / Chapter 6.3 --- Discussion --- p.68 / Chapter 6.3.1 --- Charge-Localized Forms of C5052- (C2v) and C6O6 2-(C2v) --- p.68 / Chapter 6.3.2 --- Charge-Delocalized Forms of C5052- (D5h) and C6062- (D6h) --- p.71 / Chapter 6.4 --- Conclusion --- p.72 / Chapter 6.5 --- Publication Note --- p.73 / Chapter 6.6 --- References --- p.74 / Chapter Chapter 7 --- Conclusion --- p.89 / Appendix A --- p.90 / Appendix B --- p.92

This thesis examines various reductive case studies in thermal physics. In particular, I argue that according to my account of reduction-as-construction, there are two suc- cessful examples of reduction. Thermodynamics reduces to statistical mechanics, and statistical mechanics reduces to the underlying microdynamics - be they quantum or classical. The reduction of a given theory alters that theory's scope, that is: its domain of applicability. The scope of thermodynamics will be central to this thesis - and I will argue for a narrower scope than some authors. This thesis consists of four Chapters, together with an introduction and a conclusion. In Chapter 1, I discuss how different levels of description relate to one another. I argue that a higher-level of description is reduced to the lower level, if the higher-level quantities and their behaviour can be constructed or captured by the lower-level theory. I claim that 'functionalism' can be helpful in securing reductions. In this Chapter I also argue that the aim of reduction is to vindicate, not eliminate, the higher-level theory. In Chapter 2, I tackle the reduction of thermodynamics to statistical mechanics. I articulate the functional, or nomological, role of various thermodynamic quantities that are implicitly defined by the zeroth, first and second laws of thermodynamics: temperature, energy and entropy respectively. I then argue that there are quantities in statistical mechanics that realise these roles: though finding them sometimes requires us to focus on quantum, rather than classical, statistical mechanics. In Chapter 3, I consider the reductive relationship between statistical mechanics and the underlying microdynamics. I demonstrate how the irreversible equations of statistical mechanics can be constructed from the underlying microdynamics using what I label the 'Zwanzig-Zeh-Wallace' framework. Yet this framework uses a procedure called 'coarse-graining' which has been heavily criticised in the literature; so in this Chapter I offer a justification of coarse-graining. One upshot is that the time-asymmetry in statistical mechanics is weakly emergent. In Chapter 4, I consider a question about the domain of applicability of thermal physics. Namely: does it apply to self-gravitating systems, such as elliptical galaxies? Much controversy surrounds this question: some argue yes, others argue no. I deflate the dispute by claiming that thermodynamics does not apply, but statistical mechanics does. Thus, my delineation of thermodynamics and statistical mechanics earlier in this thesis not only makes headway with the question of reduction, but also sheds light on this dispute. I argue that this situation - statistical mechanics, but without thermodynamics - can be understood in terms of a central notion in thermal physics: the thermodynamic limit. But as I also discuss: justifying this idealisation has been philosophically controversial.

Différentes études ont mis en évidence que la présence d'électrolyte modifie les performances de la nanofiltration et que l'augmentation du transfert observée est majoritairement gouvernée par la modification des propriétés du soluté (interactions soluté / électrolyte). Cependant, de nombreux verrous scientifiques et techniques restent encore à lever pour promouvoir l'intégration de ces opérations à l'échelle industrielle. Dans ce contexte, le travail proposé vise à améliorer la compréhension des mécanismes de transfert en s'appuyant d'une part sur la caractérisation multi-échelle des interactions dans les systèmes soluté neutre / électrolyte et plus particulièrement l'hydratation des espèces, et d'autre part sur la recherche de corrélations entre ces propriétés et les grandeurs de transfert. Plus précisément, il s'agit de comprendre comment les ions agissent sur les propriétés d'hydratation des sucres et leur transfert à travers une membrane de nanofiltration. Dans un premier temps, les propriétés volumiques de sucres (xylose, glucose, saccharose), qui caractérisent l'hydratation des solutés à l'échelle macroscopique, déterminées pour différentes compositions ioniques (LiCl, NaCl, KCl, Na2SO4, K2SO4, CaCl2, MgCl2, MgSO4), montrent que la déshydratation des sucres est principalement gouvernée par les interactions sucre / ions, dépendantes des propriétés des ions (valence, taille). Dans un second temps, la mécanique quantique est utilisée pour décrire les propriétés d'hydratation des ions et des sucres, seuls, puis en mélange à l'échelle microscopique. Il est montré que les sucres et les ions se déshydratent et que les sucres sont d'autant plus déshydratés que le nombre d'interactions sucre / ions augmente, qui lui-même augmente avec le nombre de coordinations des ions dans l'eau. Enfin, des corrélations quantitatives sont obtenues entre les propriétés d'hydratation des espèces (nombre d'hydratation, nombre de coordinations, nombre d'interactions...) obtenues aux différentes échelles et les grandeurs caractérisant le transfert. Ainsi, à partir de ces résultats prometteurs, des travaux complémentaires devraient permettre d'améliorer la prédiction des performances de la nanofiltration pour le traitement de solutions contenant des solutés organiques en présence d'électrolyte. / Different studies have shown that the presence of electrolyte modifies the nanofiltration performances and that the increase of the neutral solute transfer is mainly governed by the modification of the solute properties (neutral solute / electrolyte interactions). However, the development of such membrane processes is still limited since it is hardly possible to predict the process performances, In this context, the aim of this work is to study the neutral solute / electrolyte interactions using a fundamental multi scale approach in order to improve the knowledge of the transfer mechanisms taking place through nanofiltration membranes. More precisely, the objective is to understand how the ions act on the hydration properties of the saccharides and their transfer through a nanofiltration membrane. Firstly, the saccharide volumetric properties (xylose, glucose, sucrose), which characterize the solute hydration at the macroscopic scale, are determined in presence of various electrolytes (LiCl, NaCl, KCl, Na2SO4, K2SO4, CaCl2, MgCl2, MgSO4). The results show that the saccharide dehydration is due to the predominance of the saccharide / ions interactions depending on the ions' properties (valence, size). Secondly, quantum mechanics is used to describe the hydration properties of ions and saccharides, alone and then in a mixture at the microscopic scale. It is shown that both saccharide and ions are dehydrated and that the saccharides are more dehydrated for increasing saccharide / ions interactions number, which in turn increases with the ion's coordination number in water. It is also shown that the species hydration properties, obtained at different scales are consistent. Finally, quantitative correlations between the species hydration properties and the saccharide mass transfer parameters are obtained. Thus, from these promising results, further work will be devoted to improve the prediction of the performance of nanofiltration for the treatment of solutions containing organic solutes in the presence of electrolyte.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Jens Hoppe. / Ph.D.

Topological order is a new paradigm for quantum phases of matter developed to explain phase transitions which do not fit the symmetry breaking scheme for classifying phases of matter. They are characterized by patterns of entanglement that lead to topologically depended ground state degeneracy and anyonic excitations. One common approach for studying such phases in two-dimensional systems is through exactly solvable lattice Hamiltonian models such as quantum double models and String-Net models. The former can be understood as the Hamiltonian formulation of lattice gauge theories and, as such, it is defined by a finite gauge group. However, not much is known about topological phases in tridimensional systems. Motivated by this we develop a new class of three-dimensional exactly solvable models which go beyond quantum double models by using finite crossed modules instead of gauge groups. This approach relies on a lattice implementation of 2-gauge theory to obtain models with a richer topological structure. We construct the Hamiltonian model explicitly and provide a rigorous proof that the ground state degeneracy is a topological invariant and that the ground states can only be characterized with nonlocal order parameters. / Ordem topológica é um novo paradigma para fases quânticas da matéria desenvolvido para explicar transições de fase que não se encaixam no esquema de classificação de fases da matéria por quebra de simetria. Estas fases são caracterizadas por padrões de emaranhamento que levam a uma degenerescência de estado fundamental topológica e a excitações anyonicas. Uma abordagem comum para o estudo de tais fases em sistemas bidimensionais é através de modelos Hamiltonianos exatamente solúveis de rede como os modelos duplos quânticos e modelos de String-Nets. O primeiro pode ser entendido como a formulação Hamiltoniana de teorias de gauge na rede e, desta maneira, é definido por um group de gauge finito. Entretanto, pouco é conhecido a respeito de fases topológicas em sistemas tridimensionais. Motivado por isso nós desenvolvemos uma nova classe de modelos tridimensionais exatamente solúveis que vai alem de modelos duplos quânticos pelo uso de módulos cruzados finitos no lugar de grupos de gauge. Esta abordagem se baseia numa implementação em redes de teoria de 2-gauge para obter modelos com uma estrutura topológica mais rica. Nós construímos o modelos Hamiltoniano explicitamente e fornecemos uma demonstração rigorosa de que a degenerescência de estado fundamental é um invariante topológico e que os estados fundamentais só podem ser caracterizados por parâmetros de ordem não locais.

Orientador: Carlos Ourivio Escobar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T17:22:13Z (GMT). No. of bitstreams: 1 Rigolin_GustavoGarcia_D.pdf: 2659522 bytes, checksum: 04f0cc5c9d3d83caae7857516ee7a413 (MD5) Previous issue date: 2005 / Resumo: Nesta tese estudamos em detalhes uma das características da Mecânica Quântica que mais destoa de nosso senso comum: o Emaranhamento Quântico. Apresentamos uma revisão dos principais resultados obtidos no entendimento do emaranhamento, em especial do emaranhamento bipartite. Definimos formalmente o que é um estado quântico emaranhado e, em seguida, apresentamos maneiras de qualificar e quantificar este emaranhamento. Mostramos uma nova maneira de se discernir entre estados emaranhados e não emaranhados agindo apenas localmente em um dos constituintes do sistema. Apresentamos dois limitantes inferiores que nos permitem estimar o grau de emaranhamento de qualquer estado Gaussiano de dois modos. A partir de uma generalização do protocolo de teletransporte de um q bit para N q bits, criamos uma medida de emaranhamento para sistemas multipartites que possui fácil interpretação física. Estudamos também as implicações do emaranhamento na dedução das relações de incerteza de Heisenberg para sistemas de partículas idênticas. Investigamos uma possível relação entre caos e emaranhamento bipartite, onde obtemos um decréscimo no emaranhamento conforme o sistema se torna mais caótico. Finalizamos essa tese apresentando um estudo sobre o comportamento do emaranhamento a temperaturas finitas, em especial para um sistema de dois qbits descritos pela Hamiltoniana de Heisenberg xYZ / Abstract: In this dissertation we study in details one of the most astonishing features of Quantum Mechanics which totally departs from our common sense: Quantum Entanglement. We review most of what is known in the study of entanglement, specially bipartite entanglement. We formally define entanglement and, whereupon, present how to qualify and quantify entangled states. We show a novel way to distinguish between entangled and non-entangled states acting locally onto one of the constituents of the system. Then, we present two lower bounds for the entanglement of formation for arbitrary two-mode Gaussian states. Generalizing the teleportation protocol to N qubits, we create a multipartite measure of entanglement which has a simple physical interpretation and is easily computed from the state describing the system. We also study the implications of entanglement in deducing uncertainty relations for identical particles. In addition to this, we investigate the influence of chaos on the degree of bipartite entanglement in spin chains. We show that chaos decreases entanglement. We end this dissertation presenting a study about the behavior of entanglement at finite temperatures, focusing at two qubits interacting via the Heisenberg xYZ Hamiltonian / Doutorado / Física / Doutor em Ciências

Lau Kai-Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1 / Chapter 1.2 --- The G3 Method with Reduced MΦ ller-Plesset Order and Basis Set --- p.2 / Chapter 1.3 --- The Gaussian-3X Method --- p.2 / Chapter 1.4 --- The Modified G2 Method --- p.3 / Chapter 1.5 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.6 --- Remark on the Location of Transition Structures --- p.4 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.4 / Chapter Chapter 2 --- "A Gaussian-2 and Gaussian-3 Study of Alkoxide Anion Decompositions. I. H2 and CH4 Eliminations of the Methoxide, Ethoxide, i-Propoxide, and t-Butoxide Anions" --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Methods of Calcuations --- p.7 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.3.1 --- Nature of ion-neutral complex --- p.8 / Chapter 2.3.2 --- Initial bond cleavage of alkoxide anions --- p.9 / Chapter 2.3.3 --- Dissociation of alkoxide anions --- p.10 / Chapter 2.4 --- Conclusions --- p.23 / Chapter 2.5 --- Publication Note --- p.25 / Chapter 2.6 --- References --- p.25 / Chapter Chapter 3 --- A Gaussian-2 and Gaussian-3 Study of Alkoxide Anion Decompositions. II. Alkane Eliminations of (CH3)2(C2H5)CO- and (i-Pr)(C2H5)2CO- --- p.28 / Chapter 3.1 --- Introduction --- p.28 / Chapter 3.2 --- Methods of Calculations --- p.29 / Chapter 3.3 --- Results and Discussion --- p.29 / Chapter 3.3.1 --- Initial bond cleavage of alkoxide anions --- p.30 / Chapter 3.3.2 --- Dissociation of alkoxde anions --- p.31 / Chapter 3.3.3 --- General dissociation mechanism of alkoxide anions --- p.35 / Chapter 3.4 --- Conclusions --- p.37 / Chapter 3.5 --- References --- p.37 / Chapter Chapter 4 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Dimethyl Disulfide --- p.40 / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- Methods of Calculations --- p.41 / Chapter 4.3 --- Results and Discussion --- p.41 / Chapter 4.3.1 --- Bond cleavage reactions --- p.44 / Chapter 4.3.2 --- Dissociation channels involving transition structures --- p.45 / Chapter 4.4 --- Conclusions --- p.48 / Chapter 4.5 --- References --- p.48 / Chapter Chapter 5 --- A Gaussian´ؤ3 Study of the Photodissociation Channels of Propylene Sulfide --- p.50 / Chapter 5.1 --- Introduction --- p.50 / Chapter 5.2 --- Methods of Calculations --- p.51 / Chapter 5.3 --- Results and Discussion --- p.51 / Chapter 5.3.1 --- The dissociation channels involving transition structures --- p.53 / Chapter 5.3.2 --- The dissociations of sulfur atom --- p.56 / Chapter 5.4 --- Conclusions --- p.58 / Chapter 5.5 --- References --- p.59 / Chapter Chapter 6 --- Thermochemistry of Phosphorus Fluorides: A Gaussian´ؤ3 and Gaussian´ؤ3X Study --- p.60 / Chapter 6.1 --- Introduction --- p.60 / Chapter 6.2 --- Methods of Calculations --- p.62 / Chapter 6.3 --- Results and Discussion --- p.62 / Chapter 6.3.1 --- Comparison of the G3 and G3X methods --- p.62 / Chapter 6.3.2 --- Assessments of the experimental results --- p.65 / Chapter 6.4 --- Conclusions --- p.71 / Chapter 6.5 --- References --- p.71 / Chapter Chapter 7 --- Conclusions --- p.74 / Appendix A --- p.75 / Appendix B --- p.78