This thesis is concerned with quantum properties of excitonic energy transport in nanostructures that are embedded in a noisy environment. Of principal interests are ways to exploit this environment to facilitate the transport of energetic excitations. The first research chapter deals with an extension to the 'standard' open quantum system picture, where the Hilbert space is split into three: system, environment, and a wider universe. This division is natural for many biological and artificial nanostructures. A new analytical method, based on a phase space representation of the density matrix, is developed for studying such division. The effects of the wider universe are shown to be captured by a simple correction of the environmental response function. The second research chapter addresses the question: when do second-order perturbative approaches to open quantum systems, which are intuitive and simple to compute, provide adequate accuracy? A simple analytical criterion is developed, and its validity is verified for the case of the much-studied FMO dynamics as well as the canonical spin-boson model. In the third research chapter, an intuitive model of a photocell is studied. The model comprises two light-absorbing molecules coupled to an idealised reaction centre, showing asymmetric dimers are capable of providing a significant enhancement of light-to-current conversion under ambient conditions. This is done by 'parking' the energy of an absorbed photon in a dark state which neither absorbs nor emits light. In the final research chapter, a basic model for what can be thought as a "quantum brachistochrone" problem is investigated. Exotic energy configurations are found to yield considerable enhancement to the exciton's transfer probability, due to similar mechanisms studied in the previous chapter.

Orientador: Rogerio Custodio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-06T04:11:30Z (GMT). No. of bitstreams: 1 Fonseca_AndreLuizda_M.pdf: 3001049 bytes, checksum: c802c39c9c0b1345c777716076837f2d (MD5) Previous issue date: 2006 / Resumo: Monte Carlo Quântico (MCQ) é um método estocástico que possibilita a resolução da equação de Schrödinger. As duas abordagens mais utilizadas são: o Monte Carlo Variacional (MCV) e o Monte Carlo de Difusão (MCD). A implementação do MCQ apresenta resultados próximos aos valores experimentais para um grande número de sistemas. Porém, não representa corretamente estados excitados e possui uma deficiência no tratamento matemático do determinante de Slater. Uma alternativa matemática formalmente correta para tratar o determinante de Slater é possível através do conceito de matriz densidade. Neste trabalho, apresentaremos aplicações do método MCQ tradicional e com matriz densidade no nível mais elementar de modelo de ionização, que corresponde ao teorema de Koopmans. O novo tratamento teórico foi implementado e superfícies de densidade de probabilidade foram geradas para a verificação de possíveis diferenças com o método tradicional, as quais foram constatadas para sistemas atômicos e moleculares. Através das técnicas MCV e MCD utilizando as duas abordagens matemáticas foram estimadas energias de sistemas neutros e catiônicos com estados eletrõnicos de valência e de caroço, e os respectivos potenciais de ionização foram calculados para átomos e moléculas simples. As energias Hartree-Fock foram reproduzidas pelo MCV e os cálculos com MCD produziram bons resultados indicando uma alternativa extremamente simples para cálculos energéticos. Os valores encontrados para os dois tratamentos matemáticos estão próximos, com exceção de alguns estados eletrônicos de caroço, em que o cálculo tradicional não converge, enquanto o novo tratamento proposto converge normalmente. O MCV reproduziu o teorema de Koopmans para os casos estudados e o MCD corrigiu significativamente este teorema. De forma geral, o novo modelo matemático proposto, baseado na teoria de matriz densidade, apresenta resultados mais estáveis para sistemas com estados eletrônicos de camada aberta na região de caroço, confirmando que sua implementação ocorre com sucesso / Abstract: Quantum Monte Carlo (MCQ) is an stochastic method that makes possible to solve the Schrödinger equation. The two most common approachs are: the variational Monte Carlo (MCV) and diffusion Monte Carlo (MCD). The implementation of MCQ presented close results to the experimental values for a great number of systems. However, it does not represent excited states correctly and presents a deficiency in the mathematical treatment of the Slater determinant. A formally correct mathematical alternative to treat the Slater determinant is possible from the concept of density matrix. In this work, applications of traditional MCQ method and density matrix are presented in the most elementary level of ionization model corresponding to the Koopmans theorem. The new theoretical treatment is implemented and surfaces of probability density are generated for the verification of possible differences with the traditional method, which are evidenced for atomic and molecular systems. Using the MCV and MCD techniques using both mathematical approachs energies of neutral and cationic systems with valence and core eletronic states are evaluated and the respective ionization potentials are calculated for atoms and simple molecules. The Hartree-Fock energies are reproduced by MCV and the calculations with MCD produced better results indicating a extremely simple alternative for ionization calculations. The values found for both mathematical treatments are similar, except for some core eletronic states, where the traditional calculation does not converge, while the new treatment converges normally. MCV reproduces the Koopmans theorem for the cases studied and MCD improved significantly this theorem. In general, the new mathematical model based on density matrix theory, presents more reliable results for core eletronic states, suggesting a promising computational procedure / Mestrado / Físico-Química / Mestre em Ciências

Orientador: Rogerio Custodio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-04T13:27:31Z (GMT). No. of bitstreams: 1 Gomes_AndreSeveroPereira_D.pdf: 6795963 bytes, checksum: 0bb142805378a7e0eb2bddfd8984c643 (MD5) Previous issue date: 2005 / Doutorado / Físico-Química / Doutor em Quimica

Ces travaux de thèse se sont concentrés sur le développement, l'implémentation et l'application de différents types de méthodes quantiques prenant la corrélation électronique en compte, dans le but de fournir des outils performants pour la description de systèmes moléculaires à l'état fondamental et excité. La méthode dite DMRG (Density Matrix Renormalization Group) a été étudiée et un logiciel correspondant a été développé en FORTRAN. Cette méthode permet de limiter le nombre d'états électroniques à prendre en compte, ce qui fait gagner du temps de calcul, tout en assurant une précision des résultats du même ordre que celle fournie par les toutes meilleures méthodes post-Hartree-Fock actuelles. Dans la deuxième partie de cette thèse, nous avons utilisé une autre méthode : la DFT (Density Functional Theory). Une étude théorique a été effectuée sur deux fonctionnelles à séparation de portée (HISS-A et -B) afin d'évaluer dans quelle mesure ces fonctionnelles, développées au départ pour l'étude des systèmes métalliques, pouvaient être appliquées à la description de l'état fondamental et excité de systèmes moléculaires hautement conjugués. Nous avons également utilisé la DFT afin de modéliser et rationaliser le comportement photo-physique d'un composé moléculaire présentant une émission dite " duale ". Nous avons pu ainsi caractériser le comportement complexe de la molécule à l'état excité et expliquer les résultats surprenants qui avaient été observés, en particulier au niveau des spectres d'émission UV et d'excitation de fluorescence. Le phénomène d'émission duale observé a ainsi pu être lié à la présence d'un degré de liberté conformationnel important de la molécule. / In the last few years, a lot of energy has been put forward in the area of quantum chemistry to develop new methods, or to improve existing methods, that are able to describe very precisely the electronic structure of molecular systems. In this manuscript, a precise overview of such a method (namely the Density Matrix Renormalization Group, DMRG method) is given. A software able to carry out DMRG calculations has indeed been developed from scratch in the laboratory during this thesis. This method can be seen as a post-Hartree-Fock method, in which only the electronic states that are relevant for the correct description of the molecule are kept. In this way, the computational cost remains acceptable, and the results are in line with those given by "exact" methods such as full-CI. Density Functional Theory (DFT) has also been investigated in this work. DFT and TD-DFT calculations have indeed also been carried out. The performances of two middle-range-separated functionals, namely HISS-A and HISS-B, to describe electronic transitions in conjugated molecules have been probed in a theory vs. theory study. Those functionals, which had been first developed for the study of metals, show to be adequate for the correct description of electronic excitations of chromophores and of push-pull molecules. Optical properties of a dual emittor have also been studied using TD-DFT. The dual emission of this molecule has been shown to stem from the presence of two distinct emissive states, respectively of Intramolecular Charge Transfer (ICT) and locally excited (LE) nature. TD-DFT has allowed us to link those two emissive states to two different conformations of the molecule.

Les théories de champ moyen quantique représentent une base robuste pour la description de la dynamique de nombreux systèmes physiques, des noyaux aux systèmes moléculaires et aux agrégats. Cependant, le traitement incomplet des corrélations électroniques au niveau du champ moyen empêche de donner une description propre de la dynamique, en particulier la dynamique dans les régimes dissipatifs. La dissipation est intrinsèquement liée à la thermalisation qui représente le phénomène cible à d'écrire dans ce travail. Nous avons exploré un schéma purement quantique en terme des matrices densités et qui consiste en l'inclusion des corrélations de type collisions, responsables de la thermalisation dans les systèmes quantiques finis. Ceci est fait en traitant les corrélations entre deux particules avec la théorie des perturbations dépendantes du temps tout au long d'un intervalle de temps. Ceci permet de créer un ensemble d'états de type champ moyen pur pour les différentes configurations. Ces états sont traités stochastiquement dans la dynamique et fournissent en moyenne un état corrélé. Nous proposons dans ce travail une reformulation de cette théorie en terme des fonctions d'ondes où les corrélations sont traitées comme des transitions multiples de type particule-trou, limitées aux transitions deux-particules-deux-trous dans notre cas. On applique le schéma obtenu à un modèle unidimensionnel simulant de petites molécules. La capacité de cette théorie à introduire les effets dissipatifs dans le cadre du champ moyen est illustrée à travers plusieurs observables tels que les matrices à un et deux corps, les nombres d'occupation et l'entropie à un corps / Quantum mean field theories represent a robust basis for the description of many dynamical situations from nuclei to molecular systems and clusters. However, the missing of electronic correlations on top of mean field prevents them to give a proper description of the dynamics, in particular dissipative dynamics. Dissipation is intrinsically linked to thermalization which represents the target phenomenon to be described in this thesis. We thus explore a fully quantum mechanical strategy proposed in terms of density matrices in the case of nuclear collisions and which consists in the inclusion of collisional correlations responsible of thermalization in quantum finite systems. This is done by treating two body correlations in time dependent perturbation theory along a certain time span that allows to create an ensemble of pure mean field states for different configurations. These states are used into the dynamics, stochastically, providing in the average one correlated state. We propose in this work a reformulation of this theory in term of wave functions where correlations are translated into multiple particle-hole transitions, restricted to two-particles-two-holes transitions in our case. We apply the obtained scheme to a one dimensional model simulating small molecules. The ability of this theory to include dissipative effects on top of mean field is illustrated through several observables such as the one and two body density matrices, the occupation numbers and the one body entropy.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18062号 / 理博第3940号 / 新制||理||1568(附属図書館) / 30920 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 石田 憲二, 准教授 藤本 聡 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In this Bachelor thesis project, the Lindblad master equation is derived, both as the most general way of modeling interaction with an environment that lacks memory, and through microscopic derivations focused on assumptions about the way the system interacts with its environment (weak-coupling, Born-Markov and rotating wave approximations). It is then applied to a two-level system (qubit).

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No description available.

<p>This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n³). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n).</p><p>A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method.</p>