Li Chi-Lun. / 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 / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Remark on the Location of Transition Structures --- p.1 / Chapter 1.2 --- Scope of the Thesis --- p.1 / Chapter 1.3 --- References --- p.2 / Chapter Chapter 2 --- "A Gaussian-3 Study on the Photodissociation of Phenylacetylene and Formation of 1,3,5-Hexatriyne" --- p.5 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Computational Method --- p.7 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.3.1 --- Phenylacetylene → Acetylene + Benzyne --- p.8 / Chapter 2.3.2 --- "Phenylacetylene → Acetylene + (Z)-3 -Hexene- 1,5-diyne" --- p.9 / Chapter 2.3.3 --- "(Z)-3-Hexene-l,5-diyne / (E)-3 -Hexene-1,5-diyne → 1,3,5-Hexatriyne and Molecular Hydrogen" --- p.9 / Chapter 2.3.4 --- Evaluation of Thermochemical Data --- p.10 / Chapter 2.3.5 --- Evaluation of Ion Energetics Data --- p.10 / Chapter 2.4 --- Conclusions --- p.10 / Chapter 2.5 --- References --- p.11 / Chapter Chapter 3 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Cyanoethylene --- p.21 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Computational Method --- p.22 / Chapter 3.3 --- Results and Discussion --- p.23 / Chapter 3.3.1 --- Bond Cleavage Reactions --- p.23 / Chapter 3.3.2 --- Dissociation Channels Involving Transition Structures --- p.25 / Chapter 3.4 --- Conclusions --- p.25 / Chapter 3.5 --- References --- p.26 / Chapter Chapter 4 --- "A Gaussian´ؤ2 Study of Structures, Energetics, and Reactions of C2H3S- Anions" --- p.34 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Computational Method --- p.35 / Chapter 4.3 --- Results and Discussion --- p.36 / Chapter 4.3.1 --- Thioformylmethyl Anion --- p.37 / Chapter 4.3.2 --- Thioacetyl Anion --- p.37 / Chapter 4.3.3 --- Cyclic C2H3S- Ions --- p.37 / Chapter 4.3.4 --- CH2SCH- --- p.38 / Chapter 4.3.5 --- 2-Thiovinyl Anion --- p.38 / Chapter 4.3.6 --- 1-Thiovinyl Anion --- p.39 / Chapter 4.3.7 --- Intramolecular Rearrangements of 1- --- p.39 / Chapter 4.3.8 --- Intramolecular Rearrangements of Cyclic C2H3S- ions and 1´ؤThiovinyl Anion --- p.39 / Chapter 4.4 --- Conclusions --- p.40 / Chapter 4.5 --- References --- p.40 / Chapter Chapter 5 --- "Theoretical Studies of Transition Metal Complexes: Bond Energies for Fe+-D, Fe+-H2O, and Fe+-CO" --- p.51 / Chapter 5.1 --- Introduction --- p.52 / Chapter 5.2 --- Computational Method --- p.53 / Chapter 5.3 --- Results and Discussion --- p.54 / Chapter 5.3.1 --- Fe+-D --- p.54 / Chapter 5.3.2 --- Fe+-CO --- p.54 / Chapter 5.3.3 --- Fe+-H2O --- p.55 / Chapter 5.4 --- Conclusions --- p.56 / Chapter 5.5 --- References --- p.57 / Chapter Chapter 6 --- Ab Initio Study of the Charge-Delocalized and -Localized Form of the Rhodizonate Dianion --- p.61 / Chapter 6.1 --- Introduction --- p.62 / Chapter 6.2 --- Computational Method --- p.63 / Chapter 6.3 --- Results and Discussion --- p.64 / Chapter 6.3.1 --- Charge-Localized C6062- --- p.64 / Chapter 6.3.2 --- Charge-Delocalized C6062- --- p.64 / Chapter 6.4 --- Conclusions --- p.65 / Chapter 6.5 --- References --- p.66 / Chapter Chapter 7 --- "Franck-Condon Factor Simulated Spectra of the Cations of cis-2-Butene,trans-2-Butene, Isobutene, cis-Dichloroethene, and trans-Dichloroethene" --- p.71 / Chapter 7.1 --- Introduction --- p.72 / Chapter 7.2 --- Computational Method --- p.72 / Chapter 7.3 --- Results and Discussion --- p.73 / Chapter 7.3.1 --- cis-2-Butene Cation --- p.73 / Chapter 7.3.2 --- trans-2-Butene Cation --- p.74 / Chapter 7.3.3 --- cis-Dichloroethene Cation --- p.75 / Chapter 7.3.4 --- trans-Dichloroethene Cation --- p.76 / Chapter 7.3.5 --- Isobutene --- p.76 / Chapter 7.4 --- Conclusions --- p.77 / Chapter 7.5 --- References --- p.77 / Chapter Chapter 8 --- Conclusions --- p.88 / Appendix A --- p.89 / Appendix B --- p.91 / Appendix C --- p.92

Neste trabalho estudamos uma nova classe de superpotenciais em mecânica quântica supersimétrica, os quais denominamos de modulares, por serem funções do módulo da coordenada x. O superpotencial de partida proposto é da forma x |x|. Esta ideia permite tornar solúvel exatamente, a energia zero, um incontável número de potenciais gerados por estas funções no âmbito da mecânica quântica supersimétrica. Exploramos algumas aplicações para estes superpotenciais, com ênfase para uma representação da molécula de amônia supersimétrica e, em particular, mostramos que um sistema muito estudado na literatura, gerado pelo superpotencial x 1/x, pode ser resolvido mais facilmente recorrendo-se à representação modular. Procuramos estudar as soluções exatas ou aproximadas - do espectro de energias dos Hamiltonianos parceiros supersimétricos utilizando metodologias adequadas ao respectivo caso, incluindo-se o conhecido potencial x4, sendo que o método variacional de coeficientes de funções foi o que melhor se adaptou ao estudo. Este método, pouco utilizado até o momento na literatura, permitiu não apenas resolver com excelente aproximação os primeiros níveis do sistema em estudo, como também comprovou a supersimetria do sistema modular. Mostramos também que em sistemas quânticos supersimétricos, a equação de Schroedinger pode ser colocada na forma da equação de Sturm-Liouville e apresentar soluções de polinômios ortogonais, sendo que a função-peso de tais polinômios é gerada pelo superpotencial. Uma breve abordagem da simetria PT envolvendo diretamente o potencial por nós proposto também foi investigada, e mostramos que o sistema é equivalente a um Hamiltoniano não Hermitiano com potencial V(z) = (z4). / In this work we study a new class of superpotentials in supersymmetric quantum mechanics, which we call modular because of their dependence on the modulus of the x coordinate. The starting superpotential is of the form x |x|. This idea helps make exactly solvable, at zero energy, several potentials generated by these functions in the context of supersymmetric quantum mechanics. We explore some applications for these superpotenciais, with emphasis on a representation of the supersymmetric ammonia molecule and, in particular, we show that a system generated by the superpotential x-1/x, widely studied in the literature, can be solved more easily making use to the modular representation. We also seek for spectral solutions exact or approximated - of the partners Hamiltonians based on the exact ground state wave function of zero energy including the conventional x4 potential. The use of the variational method of functions coefficients. These methods, rarely used to date in the literature, allowed not only solve with excellent approximation the first levels of the system under study, but also proved the supersymmetry of the modular system. The results were compared with others found in the literature. We also show that for supersymmetric quantum systems, the Schroedinger equation can be put in a form of the Sturm-Liouville equation, and so, orthogonal polynomials solutions can be find through a weight-function generated by the superpotential. A brief overview of the PTsymmetry of the system directly involving a modular model proposed was also investigated, and we show that this system is equivalent to the non-Hermitian Hamiltonian one with potential V (z) = z4.

Apresentamos neste trabalho a primeira verificação experimental de emaranhamento entre os feixes, sinal, complementar e bombeio refletido, produzidos pelo Oscilador Paramétrico Ótico (OPO) acima do limiar. Utilizando o critério de soma de variâncias de van Loock e Furusawa, obtivemos resultados que apontam a existência de emaranhamento tripartite em nosso sistema, evidenciado através da aplicação do critério de Positividade sob Transposição Parcial de Peres-Simon (PPT). A observação desse efeito, previsto em 2006, encontrou dificuldades relacionadas a existência de um ruído clássico espúrio, inserido pelo cristal não-linear. Apresentamos, um modelo teórico para esse ruído que leva em consideração pequenas flutuações na permissividade dielétrica do cristal, associadas às vibrações da rede. Em seguida, mostramos como conseguimos controlar e reduzir o excesso de ruído de modo a obter condições que permitiram à observação do emaranhamento tripartite. / We present in this work the first experimental verification of entanglement between the, signal, idler and reflected pump beams, generated by an Optical Parametric Oscillator (OPO) above the threshold. Using the criterion of sum of variances, proposed by van Loock and Furusawa, we obtained results that indicate the existence of tripartite entanglement in our system. That is confirmed by applying the criterion of positivity under partial transposition by Peres-Simon (PPT). The observation of this effect, predicted in 2006, faced difficulties related to the existence of a spurious classical noise, introduced by the nonlinear crystal. We have also presented a theoretical model for this that takes into account small fluctuations in the dielectric permittivity of the crystal, associated with vibrations of its lattice. We show how to control and reduce the excess noise in order to achieve conditions for the observation of tripartite entanglement.

Lam Chow Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references. / Abstracts in English and Chinese. / Thesis Examination Committee --- p.i / Abstract --- p.ii / Acknowledgements --- p.iv / Table of Contents --- p.v / List of Tables --- p.vii / 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 --- Theoretical Study of Tri-s-triazine and Its Derivatives --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Methods of Calculation --- p.9 / Chapter 2.3 --- Results and Discussion --- p.9 / Chapter 2.3.1. --- Property of Tri-s-triazine --- p.9 / Chapter 2.3.2. --- Substituent Effects on the Properties of the Tri-s-triazine Parent Molecule --- p.10 / Chapter 2.3.3. --- Heats of Formation of Derivatives of Tri-s-triazine --- p.20 / Chapter 2.4 --- Conclusion --- p.22 / Chapter 2.5 --- References --- p.22 / Chapter Chapter 3 --- A Gaussian-3 Study of the Dissociative Photoionization of Acetone --- p.25 / Chapter 3.1 --- Introduction --- p.25 / Chapter 3.2 --- Methods of Calculation --- p.26 / Chapter 3.3 --- Results and Discussion --- p.26 / Chapter 3.3.1. --- "Formation of m/z = 42 (CH2CO+.),43 (CH3CO+) Ions" --- p.31 / Chapter 3.3.2. --- Formation of m/z = 43 (c-CH2CHO+) and m/z = 15 (CH3+) Ions --- p.32 / Chapter 3.3.3. --- Formation of m/z = 57 (CH3COCH2+) Ions --- p.37 / Chapter 3.3.4. --- Formation of m/z = 39 (C3H3+) Ions --- p.38 / Chapter 3.4 --- Conclusion --- p.40 / Chapter 3.5 --- Publication Note --- p.40 / Chapter 3.6 --- References --- p.40 / Chapter Chapter 4 --- "A G3(MP2) Study of the C3H60+. Isomers Fragmented from l,4-Dioxane+" --- p.42 / Chapter 4.1 --- Introduction --- p.42 / Chapter 4.2 --- Methods of Calculation --- p.43 / Chapter 4.3 --- Results and Discussion --- p.44 / Chapter 4.3.1. --- "Formation of C3H60+. Isomers 1 and 2 via Fragmentation of 1,4-Dioxane+" --- p.44 / Chapter 4.3.2. --- Reaction with Acetonitrile --- p.55 / Chapter 4.3.3. --- Reaction with Formaldehyde --- p.57 / Chapter 4.3.4. --- Reaction with Ethylene --- p.61 / Chapter 4.3.5. --- Reaction with Propene --- p.63 / Chapter 4.4 --- Conclusion --- p.67 / Chapter 4.5 --- Publication Note --- p.68 / Chapter 4.6 --- References --- p.68 / Chapter Chapter 5 --- A Computational Study of the Photodissociation Channels of Chloroiodomethane --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Methods of Calculation --- p.73 / Chapter 5.3 --- Results and Discussion --- p.74 / Chapter 5.3.1 --- CH2C1 + I(2P1/2) and CH2C1 + I(2P3/2) Channels --- p.77 / Chapter 5.3.2 --- "CH2I + C1(2P3/2,1/2) Channel" --- p.78 / Chapter 5.3.3 --- CHI + HC1 Channel --- p.80 / Chapter 5.3.4 --- CH2 + IC1 Channel --- p.81 / Chapter 5.4 --- Conclusion --- p.82 / Chapter 5.5 --- Publication Note --- p.83 / Chapter 5.6 --- References --- p.83 / Chapter Chapter 6 --- Conclusion --- p.86 / Appendix A --- p.87 / Appendix B --- p.89

The paper deals with quantum economy. It means the methods of quantum mechanics are applied in the study of economic processes. The scalar abstract economic quantities are constructed as follows: general abstract economic quantity F , average abstract economic quantity FA, marginal abstract economic quantity FM, marginal average abstract economic quantity FMA, average marginal abstract economic quantity FAM, elasticity of abstract economic quantity EF. All the abstract economic quantities mentioned above are constructed as mappings. The general theory of abstract economic quantities is utilized in a construction of the abstract total gross profit TGP. The set of static models of total gross profit TGP is constructed in the case that the first unit gross profit is slowly changed with time while the second unit gross profit is quickly changed with time in comparison with the first unit gross profit.

Desenvolvemos no presente trabalho um tratamento perturbativo para a matriz densidade reduzida de forma similar à regra áurea de Fermi para espalhamento. Aplicamos a teoria a vários exemplos e em particular reproduzimos os resultados experimentais obtidos no laboratório Kastler Brossel e obtivemos uma relação entre os tempos característicos de dissipação e decoerência. Por outro lado, desenvolvemos um modelo simples para duas moléculas interagindo com um reservatório. Mostramos resultados surpreendentes quando temos mais que dois subsistemas interagindo: no caso particular em que as moléculas estão num estado inicial coerente, bombardeadas por fontes de mesma intensidade, o estado assintótico apresenta urna concentração de energia no modo de menor frequência. Este resultado dá suporte a um modelo fenomenológico de sistemas biológicos onde a condensação de Bose- Einstein é produzida e o estado final também exibe uma concentração de energia no modo de frequência mais baixa. / In the present work we developed a perturbative treatment of reduced density matrices which is similar in spirit to Fermi\'s Golden Rule for scattering. We applied the theory to several e- xamples and in particular reproduced the results obtained in the laboratory Kastler Brossel experiment quantifying the relation between decoherence and dissipation characteristic times. On the other hand we developed a simple model for two molecules interacting through a re- servoir. We show that rather surprising results may arise when we have more than two subsys- tems in interaction: in the particular case where both molecules are initially in coherent states, if they are pumped with the same strength, the asymptotic state shows a concentraction of energy on the mode with smallest frequency. This result gives support to a phenomenological model for biological systems where a Bose- Einstein condensation is predicted and the final state also exhibits a concentration of energy in the lowest frequency mode.

Neste trabalho mostra-se que uma devida reinteração das leis da Mecânica quando formuladas como um princípio variacional define uma classe de funcionais que as satisfazem. Cada funcional define uma teoria da Mecânica, chamada Mecânica Generalizada, que descreve uma particular dinâmica. A Mecânica Clássica, que descreve uma dinâmica chamada conjuntiva, baseia-se em uma escolha chamada trivial deste funcional. Escolhas não-triviais definem teorias que descrevem dinâmicas chamadas convolutivas. Uma dessas escolhas não-triviais define uma teoria que descreve uma dinâmica convolutica que se pode chamar quântica. Essa teoria é formalmente idêntica à Mecânica Quântica mas apresenta um conteúdo epistemológico diferente. A interpretação probabilística da Mecânica Quântica surge como uma interpretação suficiente mas não necessária desse formalismo. / In this work it is shown that a proper reinterpretation of the laws of Mechanics when formulated as a variational principle defines a class of functionals wich satisfies them. Each functional defines one theory of Mechanics, called Generalized Mechanics, which describes a particular dynamics. The Classical Mechanics, which describes to so called conjunctive dynamics, is based on a trivial choice of this functiona. Non-trivial choices define theories which describe the so called convolutive dynamics. One of these non-trivial choices define a convolutive theory which may be called quantic. This theory is formally identical to Quantum Mechanics but it displays a different epistemological content. The probabilistic interpretation of Quantum Mechanics emerges as a sufficient but not necessary interpretation of this formalism.

Neste trabalho estudamos as propriedades de emaranhamento dos estados de dois quasifótons de frequências diferentes, fazendo a aproximação de que o vácuo de quasifótons é igual ao vácuo de fótons, no caso em que não temos campo externo algum e no caso da presença de um campo magnético externo, constante e homogêneo. Estudamos também as propriedades de emaranhamento do próprio vácuo de quasifótons e dos estados de dois quasifótons no caso monocromático, sem campo externo e com o vácuo de quasifótons levado em conta exatamente. / In this work we study the properties of entanglement of the states of two quasi-photons of different frequencies, considering the approximation that the quasi-photon\'s vacuum is equal the photon\'s vacuum, in the case where we have no external field and in the case where we have an external, constant and homogeneous magnetic field. We study also the properties of entanglement of the quasi-photon\'s vacuum and of the states of two quasi-photons in the monochromatic case, without external field and with the quasi-photon\'s vacuum considered exactly.

This work is focused on the different supersymmetric extensions of the Landau model. We aim to fully solve each model and describe its energy levels, wavefunctions, Hilbert space and define a norm on it, as well as find symmetry generators and transformations with respect to them. Several possible generalizations were considered before. It was found for Landau model on the so called Superflag manifold as well as planar Superflag and Superplane Landau models that standard norm on the Hilbert space is not positive definite. Later for planar cases it was found that it is possible to fix this by introducing a new norm which will be invariant and positive definite. Surprisingly this procedure brings up "hidden" symmetries for the known super Landau models. In the dissertation we apply the same procedure for Landau model on superpshere and Superflag manifolds. It turns out that superpsherical Landau model is equivalent to the Superflag model with one of the parameters fixed. Because the model on superpshere can be recovered from the Superflag we will do calculations of corrected norm only for the Superflag. After this we develop a different generalization of the Superplane Landau model. Starting with Lagrangian in a superfield form we introduce two arbitrary functions of superfields K(Φ) and V(Φ) into the Lagrangian. We follow with the component form of Lagrangian. The quantization of the model is possible, and we will show that there is a reparametrization which turn equation of motion of the first scheme into the second set. Standard metric is again non-positive definite and we apply already known procedure to correct it. It will not be possible to solve Schrodinger equations in general with undefined K and V, so we consider one specific case which give us Landau model on a sphere with N = 2 supersymmetry, which put it apart from the superspherical Landau model, which have a superpshere for a target space but do not possess supersymmetry.

Relations between propagators and Green functions of Hamiltonians which are SUSY partners have been obtained. New exact propagators for the family of multi-well, time-dependent and non-hermitian potentials have been calculated. Non-conservative SUSY transformation has been studied in the case of multichannel Schrodinger equation with different thresholds. Spectrum (bound/virtual states and resonances) of the non-conservative SUSY partner of zero potential has been founded. Exactly solvable model of the magnetic induced Feshbach resonance has been constructed. This model was tested in the case of Rb$^{85}$. Conservative SUSY transformations of the first and the second order have been studied in the case of multichannel Schrodinger equation with equal thresholds. Transformations which introduce non-trivial coupling between scattering channels have been founded. The first order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter has been founded in the case of two channel scattering with partial waves of different parities. In the case of coinciding parities we have found the second order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter. Phenomenological two channel $^3S_1-^3D_1$ neutron-proton potential has been obtained by using single channel, phase equivalent and coupling SUSY transformations applied to zero potential.