[pt] A dissertação tem por objetivo mostrar a importância e a significação da referência à filosofia grega no pensamento de Werner Heisenberg, um dos principais fundadores da mecânica quântica. A referência aos gregos, constante em seus escritos, deve ser primeiramente situada no contexto da crítica à modernidade, uma das diretrizes herdadas de Niels Bohr e uma das características mais fundamentais da filosofia de Heisenberg. Isto é, o pensamento grego é, para Heisenberg, um contraponto aos fundamentos da filosofia moderna, cujos limites são intransponíveis no que diz respeito à compreensão dos problemas apresentados pela física moderna. Acreditamos, no entanto, ser possível afirmar que as constantes referências, sobretudo a Platão e Aristóteles, têm também um papel fundamental no que diz respeito à caracterização do nível de realidade próprio à mecânica quântica. / [en] This dissertation has for objective to show the importance and signification of the reference to the greek philosophy in the thought of Werner Heisenberg, one of the main founders of quantum mechanics. The reference to the greek philosophy, constant in his writings, must first be situated in the context of the critics to modernity, one of the inherited lines of direction of Niels Bohr and one of the most basic characteristics of Heisenberg`s philosophy. That is, the greek thought is, for Heisenberg, a counterpoint to the beddings of the modern philosophy, whose limits are insurmountable with respect to the understanding of the problems presented for the modern physics. We believe, however, that is possible to affirm that the constant references, especially to Plato and Aristotle, have also a fundamental role with respect to the characterization of the level of reality proper to the quantum mechanics.

[pt] A teoria da gravidade quântica em laços (loop quantum gravity ou LQG) é atualmente uma das mais promissoras abordagens para descrever a relatividade geral em termos quânticos. Um dos problemas-chave é detectar na teoria quântica estados semiclássicos, que apresentem propriedades macroscópicas iguais às de configurações específicas da teoria clássica. Nesta dissertação, começamos apresentando o formalismo da LQG e sua interpretação física. Do ponto de vista matemático, a LQG pode ser pensada como uma quantização canônica de uma teoria de gauge de SU(2) em uma 3-variedade. No entanto, diferentemente da abordagem usual, que gera uma representação apenas por operadores auto-adjuntos, a abordagem polimérica da LQG gera uma representação mista que usa operadores auto-adjuntos e unitários. Tomamos então um modelo polimérico, análogo à LQG, do sistema físico mais simples: o movimento unidimensional de uma partícula pontual. Neste contexto, desenvolvemos um arcabouço que resolve o problema dos estados semiclássicos, que são estudados em detalhe. Finalmente, consideramos a quantização polimérica do campo eletromagnético livre, resultando numa teoria abeliana muito similar à LQG. Neste contexto, o mesmo arcabouço desenvolvido para o caso anterior pode ser aplicado. / [en] Loop quantum gravity (LQG) is currently one of the most promising approaches to describing general relativity in quantum terms. One of its key issues is to detect in the quantum theory semiclassical states whose macroscopic properties are the same as those of specific configurations of the classical theory. In this dissertation, we begin by presenting the LQG formalism and its physical interpretation. From a mathematical point of view, LQG can be thought of as a canonical quantization of a SU(2) gauge theory in a 3-manifold. However, whereas the usual approach generates a representation exclusively by self-adjoint operators, LQG's polymer approach generates a mixed representation using both self- adjoint and unitary operators. We then take a polymer model, analogous to LQG, of the simplest physical system: the one-dimensional movement of a point particle. In this context, we develop a framework that solves the problem of semiclassical states, which are studied in detail. Finally, we consider the polymer quantization of the free electromagnetic field, which results in an abelian theory which is very similar to LQG. In this context, it is possible to apply the same framework that was developed for the previous case.

We formulate a process of quantization of classical mechanics, from a symplecticperspective. The Dirac quantization axioms are stated, and a satisfactory prequantizationmap is constructed using a complex line bundle. Using polarization, it isdetermined which prequantum states and observables can be fully quantized. Themathematical concepts of symplectic geometry, fibre bundles, and distributions are exposedto the degree to which they occur in the quantization process. Quantizationsof a cotangent bundle and a sphere are described, using real and K¨ahler polarizations,respectively.

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A series of para-substituted phenylethylamine analogues bound to the enzyme aromatic amine dehydrogenase have been simulated using quantum mechanical electronic structure calculations and molecular mechanical molecular dynamics simulations. Trends have been verified connecting bond dissociation energy (and thus driving force) to observed rate constants and activation enthalpy. Trends have been identified in connecting statistics drawn from molecular dynamics simulations and the temperature dependence of the kinetic isotope effect, notably that as the temperature dependence of the kinetic isotope effect increases the flexibility of the promoting vibration decreases. This is explained as being more effected by thermal energy put into the system, and therefore more affected by temperature.

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.

Many of the bands in the vapor-phase far-ultraviolet absorption spectra of simple molecules can often be fit to mathematical progressions referred to as molecular Rydberg series. The name Rydberg arises from the similarity between the Rydberg formula for the atomic hydrogen spectrum and the formulae for the progressions found in molecular spectra. The theories of molecular Rydberg transitions and states are discussed in terms of the inferences that have been made in the past from the available spectral data. The dipole moment changes (ca. 0.4 Debye units) from the ground state to all of the Rydberg states studied were found to be smaller than changes typically found in transitions of charge-transfer nature (ca. 1 Debye unit). The implication is that the Rydberg transitions are fairly localized. The changes in polarizability are on the order of 6 x 10⁻²⁴ cm³ and are assumed to be increases over those of the ground state.

京都大学 / 0048 / 新制・課程博士 / 博士(文学) / 甲第22182号 / 文博第829号 / 新制||文||688(附属図書館) / 京都大学大学院文学研究科現代文化学専攻 / (主査)准教授 伊勢田 哲治, 教授 伊藤 和行, 准教授 大塚 淳 / 学位規則第4条第1項該当 / Doctor of Letters / Kyoto University / DGAM

This research investigates characteristics of PT (parity-time) symmetry breaking in a system of two optically-coupled, time-delayed semiconductor lasers. A theoretical rate equation model for the lasers’ electric fields is presented and then reduced to a 2x2 Hamiltonian model, which, in the absence of time-delay, is PT-symmetric. The important parameters we control are the temporal separation of the lasers (τ), the frequency detuning (∆ω), and the coupling strength (κ). The detuning is experimentally controlled by varying the lasers’ temperatures, and intensity vs. ∆ωbehavior are examined, specifically how the PT-transition and the period and amplitude of sideband intensity oscillations change withκandτ. Experiments are compared to analytic predictions and numerical results, and all are found to be in good agreement. Eigenvalues, eigenvectors, and exceptional points of the reduced Hamiltonian model are numerically and analytically investigated, specifically how nonzero delay affects existing exceptional points.