Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-29T15:51:25Z (GMT). No. of bitstreams: 1 Veronez_Matheus_D.pdf: 15544434 bytes, checksum: 608af036b8db9a50a1b8ed957b506d84 (MD5) Previous issue date: 2015 / Resumo: Representações no espaço de fase são ferramentas bastante difundidas no estudo e na simulação de sistemas quânticos, principalmente devido aos seus apelos clássicos. Tanto na mecânica quântica quanto na clássica, elementos similares, tal como densidades de probabilidade, podem ser definidos e usados para comparar ambos regimes. Neste trabalho construímos a partir de primeiros princípios uma corrente quântica no espaço de fase na representação de estados coerentes canônicos. Determinamos a corrente quântica para sistemas sob evolução de uma hamiltoniana genérica e mostramos que ela pode ser expandida numa série de potências em $hbar$ cujo termo de ordem mais baixa é a corrente clássica. Calculamos analiticamente a corrente para alguns sistemas uni-dimensionais simples. A corrente quântica apresenta propriedades não-clássicas, por exemplo, inversão de momento e surgimento de novos pontos de estagnação aos pares durante a dinâmica. Mostramos que estes pares são compostos por um ponto de sela, que é um zero da densidade de probabilidade e possui uma carga topológica de -1, e por um vórtice, que possui carga +1. Ambos pontos constituem o que denominamos dipolo topológico. Analisamos o papel destes dipolos no espalhamento de uma partícula por uma barreira gaussiana e mostramos que suas localizações em relação às superfícies de energia clássicas e em relação aos máximos da densidade de probabilidade são assinaturas de tunelamento / Abstract: Phase space representations are widely used tools to study and simulate the quantum dynamics of systems, mainly due to its natural classical appeal. In both classical and quantum mechanics, corresponding but not equivalent structures, such as probability densities, can be defined and explored to compare both dynamical regimes. In this work, we constructed from first principles the quantum phase space current for a quantum system in the canonical coherent states representation. We determined the quantum current for systems evolving under a general Hamiltonian, and we showed that the current can be expanded as a power series in $hbar$, whose lowest order term is the classsical current. We also calculated analytically the quantum current for simple one-dimensional systems. The quantum current presents non-classical features, such as momentum inversion and emergence of new stagnation points which appear in pairs during the dynamics. We showed that the pairs are composed by a saddle point, which is a zero of the phase space probability density and bears a topological charge -1, and a vortex, with charge +1. Both points constitute what we named a topological dipole. We analysed the role the dipoles play in the scattering of a particle by a gaussian barrier, and we showed that the location of the dipoles in relation to the classical energy surfaces and the quantum probability density maxima is a fingerprint of quantum tunneling / Doutorado / Física / Doutor em Ciências / 2013/02248-0 / 157615/2011-1 / FAPESP / CNPQ

Neste trabalho, a reação O(3P) + HBr → OH + Br, que se insere no contexto da química atmosférica, mais especificamente nos ciclos de destruição catalítica do ozônio, foi estudada empregando superfícies de energia potencial ab initio de alta qualidade. Construímos superfícies para os estados eletrônicos 3A\" e 3A\', baseadas na expansão de muitos corpos, com potenciais de dois corpos ajustados por funções \"switched-MLJ\" e potenciais de três corpos interpolados utilizando o método RKHS. Os pontos ab initio utilizados foram obtidos no nível de teoria MRCISD+Q/CBS+SO. A superfície final para o estado eletrônico 3A\" foi corrigida por um fator multiplicativo de modo que reproduzisse cálculos benchmark para a altura de barreira, em que foram considerados efeitos relativísticos (escalares e spin-órbita), correlação caroço-valência e correlação de ordem alta (excitações triplas e quádruplas). As principais características da SEP 3A\" são dois mínimos de van der Walls no canal de entrada e saída e um estado de transição com uma barreira energética de 5,01 kcal mol-1. A SEP 3A\' tem um estado de transição linear em 6,45 kcal mol-1. O valor obtido para a entalpia de reação, a 0 K, foi de -15,7 kcal mol-1, muito próximo do valor experimental de -15,14 kcal mol-1. Calculamos constantes de velocidade, no intervalo de 200 a 1000 K, utilizando a teoria do estado de transição variacional com contribuições de tunelamento multidimensional (ICVT/µOMT) e com uma aproximação de espalhamento reativo quântico (QM/JS). Estes valores estão em ótima concordância com os dados experimentais da literatura, em todo intervalo de temperatura em que estão disponíveis: de 221 a 554 K para reação O + HBr e de 295 a 419 K para reação O + DBr. As constantes de velocidade, a 298 K e em cm3 molécula-1 s-1, obtidas para a reação O + HBr são: 3,62·10-14 (ICVT/µOMT) e 3,35·10-14 (QM/JS), enquanto que o valor experimental é 3,78·10-14. A qualidade destes resultados reforça nossa confiança nos procedimentos e aproximações utilizadas, abrindo caminho para a caracterização, em alto nível, de uma grande variedade de reações em fase gasosa. / In this work, the O(3P) + HBr → OH + Br reaction, which is relevant to atmospheric chemistry, specially for the catalytic ozone depletion, was studied using high-level ab initio potential energy surfaces. We constructed surfaces for the 3A\" and 3A\' electronic states, based on the many-body expansion, with the two-body potentials adjusted by the switched-MLJ function and the three-body potentials interpolated using the RKHS method. The ab initio points were calculated at the MRCISD+Q/CBS+SO level of theory. The main features of the 3A\" are the presence of two van der Waals minima, at the entrance and exit channels, and a transition state with a barrier height of 5.01 kcal mol-1. The 3A\' PES has a linear transition state at 6.45 kcal mol-1. We obtained the enthalpy of reaction, at 0 K, of -15.7 kcal mol-1, in close agreement with the experimental value of -15.14 kcal mol-1. Rate constants, in the temperature range from 200 to 1000 K, were calculated using the variational transition state theory with contributions of multidimensional tunneling (ICVT/µOMT) and also a quantum reactive scattering approach (QM/JS). Their values are in fair agreement with the experimental data in the literature in the whole temperature range available: from 221 to 554 K for the O + HBr reaction, and from 295 to 419 K for the O + DBr reaction. At 298 K, the calculated rate constants, in cm3 molecule-1 s-1, for the O + HBr reaction are 3.62·10-14 (ICVT/µOMT) and 3.35·10-14 (QM/JS); and the experimental value is 3.78·10-14. The quality of these results reinforces our confidence in the procedures and approximations used, leading to the possibility of high-level characterization of a variety of gas phase reactions.

In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. We also classify the inverse to the Hamiltonian operator as a Schatten-von Neumann operator. Finally, we derive the fundamental solution to the Schrödinger Equation corresponding to the Harmonic Oscillator using Mehler’s formula.

We are interested in complex electronic structures of various atomic and ionics systems. We use an ab initioapproach, the multiconfigurational Dirac-Hartree-Fock (MCDHF), to compute atomic structures and properties.We contribute in three main ways to the already existent literature: by developing and implementing originalcomputer programs, by investigating possibilities of alternative computational methodologies and strategies, andfinally by performing accurate atomic structure calculations to support other research fields, i.e. nuclear physics,astrophysics or experimental physics, through the theoretical estimation of relevant atomic data.We raise questions about the choice of the optimal orbital basis by considering finite basis sets, MCDHF orbitalbases and natural-orbital bases. We demonstrate the promising potential of the latter in the context of hyperfinestructures and hope that others will find interest in pursuing our analysis. Ultimately, our work put forward someweaknesses of the traditional optimization strategy based on the layer-by-layer optimization strategy.We also perform large-scale calculations to determine accurate atomic properties such as energy levels, hyperfinestructures, isotope shifts, transition parameters, radiative lifetimes and Landé g factors. We show through thevariety of atomic properties and atomic systems studied, the difficulty of describing, in the relativistic framework,the correlation between the spatial position of electrons due to their Coulomb repulsion.This thesis is organized in two main parts. The first one is dedicated to the theoretical and computationalbackgrounds that are needed to understand the theoretical models and the interpretation of our results. Thesecond part presents and summarizes our articles and manuscripts. They are separated in four groups, A, B, C,and D, around the themes of the atomic orbital bases, the applications to nuclear physics, the applications toastrophysics, and investigations of negative ions. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

While the spin trapping properties of thiols have been investigated through EPR analysis and kinetics studies, few groups have studied these properties using strictly computational methods. In particular, α-lipoic acid (ALA) and its reduced form, dihydrolipoic acid (DHLA), one of the strongest endogenously produced antioxidants, show potential for being effective, naturally occurring spin traps for the trapping of reactive oxygen species. This research covers electronic structure calculations of ALA, DHLA, and their corresponding hydroxyl radical spin adducts, performed at the cc-pVDZ/B3LYP/DFT level of theory. The effects on DHLA introduced by other radicals such as ·OOH, ·OCH3, and ·OOCH3 are reported. Explicit solvation was carried out using open-source molecular packing software and was studied using MOPAC PM6 semi-empirical geometry optimizations. Complete Basis Set (CBS) limit extrapolations were performed using cc-pVXZ (X = D, T, Q) Dunning basis sets under the DFT/B3LYP level of theory, and results are compared to the literature.

<div> Challenges in the semiconductor industry have resulted in the discovery of a plethora of promising materials and devices such as the III-Vs (InGaAs, GaSb, GaN/InGaN) and 2D materials (Transition-metal dichalcogenides [TMDs]) with wide-ranging applications from logic devices, optoelectronics to biomedical devices. Performance of these devices suffer significantly from scattering processes such as polar-optical phonons (POP), charged impurities and remote phonon scattering. These scattering mechanisms are long-ranged, and a quantitative description of such devices require non-local scattering calculations that are computationally expensive. Though there have been extensive studies on coherent transport in these materials, simulations are scarce with scattering and virtually non-existent with non-local scattering. </div><div> </div><div>In this work, these scattering mechanisms with full non-locality are treated rigorously within the Non-Equilibrium Green's function (NEGF) formalism. Impact of non-locality on charge transport is assessed for GaSb/InAs nanowire TFETs highlighting the underestimation of scattering with local approximations. Phonon, impurity scattering, and structural disorders lead to exponentially decaying density of states known as Urbach tails/band tails. Impact of such scattering mechanisms on the band tail is studied in detail for several bulk and confined III-V devices (GaAs, InAs, GaSb and GaN) showing good agreement with existing experimental data. A systematic study of the dependence of Urbach tails with dielectric environment (oxides, charged impurities) is performed for single and multilayered 2D TMDs (MoS2, WS2 and WSe2) providing guideline values for researchers. </div><div><br></div><div>Often, empirical local approximations (ELA) are used in the literature to capture these non-local scattering processes. A comparison against ELA highlight the need for non-local scattering. A physics-based local approximation model is developed that captures the essential physics and is computationally feasible.</div>

Le ZX-Calculus est un langage graphique puissant et intuitif, issu de la théorie des catégories, et qui permet de raisonner et calculer en quantique. Les évolutions quantiques sont vues dans ce formalisme comme des graphes ouverts, ou diagrammes, qui peuvent être transformés localement selon un ensemble d’axiomes qui préservent le résultat du calcul. Un aspect des plus importants du langage est sa complétude : Étant donnés deux diagrammes qui représentent la même évolution quantique, puis-je transformer l’un en l’autre en utilisant seulement les règles graphiques permises par le langage ? Si c’est le cas, cela veut dire que le langage graphique capture entièrement la mécanique quantique. Le langage est connu comme étant complet pour une sous-classe (ou fragment) particulière d’évolutions quantiques, appelée Clifford. Malheureusement, celle-ci n’est pas universelle : on ne peut pas représenter, ni même approcher, certaines évolutions. Dans cette thèse, nous proposons d’élargir l’ensemble d’axiomes pour obtenir la complétude pour des fragments plus grands du langage, qui en particulier sont approximativement universels, voire universels. Pour ce faire, dans un premier temps nous utilisons la complétude d’un autre langage graphique et transportons ce résultat au ZX-Calculus. Afin de simplifier cette fastidieuse étape, nous introduisons un langage intermédiaire, intéressant en lui-même car il capture un fragment particulier mais universel de la mécanique quantique : Toffoli-Hadamard. Nous définissons ensuite la notion de diagramme linéaire, qui permet d’obtenir une preuve uniforme pour certains ensembles d’équations. Nous définissons également la notion de décomposition d’un diagramme en valeurs singuliaires, ce qui nous permet de nous épargner un grand nombre de calculs. Dans un second temps, nous définissons une forme normale qui a le mérite d’exister pour une infinité de fragments du langage, ainsi que pour le langage lui-même, sans restriction. Grâce à cela, nous reprouvons les résultats de complétude précédents, mais cette fois sans utiliser de langage tiers, et nous en dérivons de nouveaux, pour d’autres fragments. Les états contrôlés, utilisés pour la définition de forme normale, s’avèrent en outre utiles pour réaliser des opérations non-triviales telles que la somme, le produit terme-à-terme, ou la concaténation. / The ZX-Calculus is a powerful and intuitive graphical language, based on category theory, that allows for quantum reasoning and computing. Quantum evolutions are seen in this formalism as open graphs, or diagrams, that can be transformed locally according to a set of axioms that preserve the result of the computation. One of the most important aspects of language is its completeness: Given two diagrams that represent the same quantum evolution, can I transform one into the other using only the graphical rules allowed by the language? If this is the case, it means that the graphical language captures quantum mechanics entirely. The language is known to be complete for a particular subclass (or fragment) of quantum evolutions, called Clifford. Unfortunately, this one is not universal: we cannot represent, or even approach, certain quantum evolutions. In this thesis, we propose to extend the set of axioms to obtain completeness for larger fragments of the language, which in particular are approximately universal, or even universal. To do this, we first use the completeness of another graphical language and transport this result to the ZX-Calculus. In order to simplify this tedious step, we introduce an intermediate language, interesting in itself as it captures a particular but universal fragment of quantum mechanics: Toffoli-Hadamard. We then define the notion of a linear diagram, which provides a uniform proof for some sets of equations. We also define the notion of singular value decomposition of a diagram, which allows us to avoid a large number of calculations. In a second step, we define a normal form that exists for an infinite number of fragments of the language, as well as for the language itself, without restriction. Thanks to this, we reprove the previous completeness results, but this time without using any third party language, and we derive new ones for other fragments. The controlled states, used for the definition of the normal form, are also useful for performing non-trivial operations such as sum, term-to-term product, or concatenation.

This thesis uses previously proposed methodology for simulations of all-trans- polyenes with conjugated systems. Dynamic properties, especially the mean lifeti- mes of the excited states, of these molecules were systematically simulated. Obta- ined data shows that the method is still too time-consuming for polyene molecules with more than 20 carbon atoms, including most carotenoids. Thus, a study of active space reduction was performed with the model tetradecaheptaene molecule with regards to excited state mean lifetimes. A new, less time-consuming method would need further simulation studies. Moreover, static spectra of the these mo- lecules were studied as well, yielding a comparison of different DFT and ab-initio approaches. 1

This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

The on-surface reactions of 10-bromo-10'-(2,6-dimethylphenyl)-9,9'-bianthracene on Au(111) surface have been investigated by a combination of bond-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, and tightbinding and mean-field Hubbard calculations. The reactions afford the synthesis of two open-shell nanographenes (1a and 1b) exhibiting different scenarios of all-carbon magnetism. 1a, an allbenzenoid nanographene with previously unreported triangulenelike termini, contains a high proportion of zigzag edges, which endows it with an exceedingly low frontier gap of 110 meV and edge-localized states. The dominant reaction product (1b) is a non-benzenoid nanographene consisting of a single pentagonal ring in a benzenoid framework. The presence of this nonbenzenoid topological defect, which alters the bond connectivity in the hexagonal lattice, results in a non-Kekulé nanographene with a spin S = ½, which is detected as a Kondo resonance. Our work provides evidence of all-carbon magnetism, and motivates the use of topological defects as structural elements toward engineering agnetism in carbon-based nanomaterials for spintronics.