En la literatura sobre mecànica quàntica és freqüent trobar descriptors basats en la densitat de parells o la densitat electrònica, amb un èxit divers segons les aplicacions que atenyin. Per tal de que tingui sentit químic un descriptor ha de donar la definició d'un àtom en una molècula, o ésser capaç d'identificar regions de l'espai molecular associades amb algun concepte químic (com pot ser un parell solitari o zona d'enllaç, entre d'altres). En aquesta línia, s'han proposat diversos esquemes de partició: la teoria d'àtoms en molècules (AIM), la funció de localització electrònica (ELF), les cel·les de Voroni, els àtoms de Hirshfeld, els àtoms difusos, etc.L'objectiu d'aquesta tesi és explorar descriptors de la densitat basats en particions de l'espai molecular del tipus AIM, ELF o àtoms difusos, analitzar els descriptors existents amb diferents nivells de teoria, proposar nous descriptors d'aromaticitat, així com estudiar l'habilitat de totes aquestes eines per discernir entre diferents mecanismes de reacció. / In the literature, several electronic descriptors based in the pair density or the density have been proposed with more or less success in their pratical applications. In order to be chemically meaningful the descriptor must give a definition of an "atom" in a molecule, or instead be able to identify some chemical interesting regions (such as lone pair, bonding region, among others). In this line, several molecular partition schemes have been put forward: atoms in molecules (AIM), electron localization function (ELF), Voronoi cells, Hirshfeld atoms, fuzzy atoms, etc. The goal of this thesis is to explore the density descriptors based on the molecular partitions of AIM, ELF and fuzzy atom, analyze the existing decriptors at several levels of theory, propose new aromaticity descriptors, and study its ability to discern between different mechanisms of reaction.

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Die Zeitverzögerung bei der Streuung in zwei Dimensionen ist eine Funktion von zwei unabhängigen Parametern. Wenn diese Funktion Sattelpunkte aufweist, so hat der entsprechende Funktionswert theoretisch ein unendlich großes Gewicht in der Wahrscheinlichkeitsverteilung der Zeitverzögerungen. Dieser Zusammenhang soll analytisch und numerisch nachgewiesen und detailliert beschrieben werden. Insbesondere soll die klassische und quantenmechanische Wahrscheinlichkeitsverteilung der Zeitverzögerung für ein Modellsystem aus mehreren nichtüberlappenden zentralsymmetrischen Potentialen berechnet werden. Erwartete Ergebnisse sind Aussagen über die Parameterwerte, bei denen der oben genannte Effekt zu beobachten ist sowie Näherungsformeln für die Verteilung der Zeitverzögerung in der Nähe der Singularitäten. Außerdem soll die quantenmechanisch zu erwartende Glättung der Verteilungsfunktion quantitativ beschrieben werden. / For scattering problems in two dimensions, time-delay is a function of two independent parameters. If this function features saddle points, the corresponding function value should theoretically have an infinite weight in the probability distribution of time-delays. This correlation shall be confirmed analytically and numerically and studied in-depth. In particular, the classical and quantum-mechanical probability distribution of time-delays shall be calculated for a model system consisting of multiple non-overlapping potentials with rotational symmetry. We expect to obtain information about the parameter values where the aforementioned effects can be observed, and analytical approximations for the time-delay distribution near the singularities. Furthermore, the smoothing of the distribution in the quantummechanical regime shall be quantified.

In this thesis we numerically compute the scattering lengths and bound states for sodium-rubidium collisions at low energy. This work was motivated by experiments which aim to produce Bose-Einstein condensates (BEC) mixtures of sodium-rubidium. Elastic collision properties are important for the rethermalization of the atoms during the evaporative cooling process. Inelastic processes, which we also discuss to some extent, cause trap losses in those experiments. In order to reach the required temperature and density the elastic collision rates should be sufficiently large compared to the inelastic rates. The scattering lengths, which completely specify the elastic collision parameters at low energy, determine the miscibility and phase diagram of the sodium-rubidium condensate mixture. We calculate the scattering lengths approximately and find agreement with previous calculations indicating that miscible phases of sodium and rubidium condensates do not appear to be feasible in the absence of external fields.

Thesis (Ph.D.); Submitted to the University of California, Berkeley, CA (US); 21 Dec 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56768" Urban, Jeffry Todd. USDOE Director. Office of Science. Office of Basic Energy Sciences (US) 12/21/2004. Report is also available in paper and microfiche from NTIS.

Cette thèse étudie deux modèles de calcul: les marches quantiques (QW) et les automates cellulaires quantiques (QCA), en vue de les appliquer en simulation quantique. Ces modèles ont deux avantages stratégiques pour aborder ce problème: d'une part, ils constituent un cadre mathématique privilégié pour coder la description du système physique à simuler; d'autre part, ils correspondent à des architectures expérimentalement réalisables.Nous effectuons d'abord une analyse des QWs en tant que schéma numérique pour l'équation de Dirac, en établissant leur borne d'erreur globale et leur taux de convergence. Puis nous proposons une notion de transformée de Lorentz discrète pour les deux modèles, QW et QCA, qui admet une représentation diagrammatique s'exprimant par des règles locales et d'équivalence de circuits. Par ailleurs, nous avons caractérisé la limite continue d'une grande classe de QWs, et démontré qu'elle correspond à une classe d'équations aux dérivées partielles incluant l'équation de Dirac massive en espace-temps courbe de $(1+1)$-dimensions.Finalement, nous étudions le secteur à deux particules des automates cellulaires quantiques. Nous avons trouvé les conditions d'existence du spectre discret (interprétable comme une liaison moléculaire) pour des interactions à courte et longue portée, à travers des techniques perturbatives et d'analyse spectrale des opérateurs unitaires. / This thesis is devoted to the development of two well-known models of computation for their application in quantum computer simulations. These models are the quantum walk (QW) and quantum cellular automata (QCA) models, and they constitute doubly strategic topics in this respect. First, they are privileged mathematical settings in which to encode the description of the actual physical system to be simulated. Second, they offer an experimentally viable architecture for actual physical devices performing the simulation.For QWs, we prove precise error bounds and convergence rates of the discrete scheme towards the Dirac equation, thus validating the QW as a quantum simulation scheme. Furthermore, for both models we formulate a notion of discrete Lorentz covariance, which admits a diagrammatic representation in terms of local, circuit equivalence rules. We also study the continuum limit of a wide class of QWs, and show that it leads to a class of PDEs which includes the Hamiltonian form of the massive Dirac equation in (1+1)-dimensional curved spacetime.Finally, we study the two particle sector of a QCA. We find the conditions for the existence of discrete spectrum (interpretable as molecular binding) for short-range and for long-range interactions. This is achieved using perturbation techniques of trace class operators and spectral analysis of unitary operators.

Light-harvesting in nature is known to work differently than conventional man-made solar cells. Recent studies found electronic excitations, delocalised over several chromophores, and a soft, vibrating structural environment to be key schemes that might protect and direct energy transfer yielding increased harvest efficiencies even under adversary conditions. Unfortunately, testing realistic models of noise assisted transport at the quantum level is challenging due to the intractable size of the environmental wave function. I developed a powerful tree tensor network states (TTNS) method that finds an optimally compressed explicit representation of the combined electronic and vibrational quantum state. With TTNS it is possible to simulate exciton-phonon quantum dynamics from small molecules to larger complexes, modelled as an open quantum system with multiple bosonic environments. After benchmarking the method on the minimal spin-boson model by reproducing ground state properties and dynamics that have been reported using other methods, the vibrational quantum state is harnessed to investigate environmental dynamics and its correlation with the spin system. To enable simulations of realistic non-Born-Oppenheimer molecular quantum dynamics, a clustering algorithm and novel entanglement renormalisation tensors are employed to interface TTNS with ab initio density functional theory (DFT). A thereby generated model of a pentacene dimer containing 252 vibrational normal modes was simulated with TTNS reproducing exciton dynamics in agreement with experimental results. Based on the environmental state, the (potential) energy surfaces, underlying the observed singlet fission dynamics, were calculated yielding unprecedented insight into the super-exchange mediated avoided crossing mechanism that produces ultrafast and high yield singlet fission. This combination of DFT and TTNS is a step towards large scale material exploration that can accurately predict excited states properties and dynamics. Furthermore, application to biomolecular systems, such as photosynthetic complexes, may give valuable insights into novel environmental engineering principles for the design of artificial light-harvesting systems.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-01T20:10:46Z No. of bitstreams: 1 REX ANTONIO COSTA MEDEIROS - DISSERTAÇÃO PPGEE 2004..pdf: 14601327 bytes, checksum: 5e8b5fae1a59cd77236adc8cc0655c17 (MD5) / Made available in DSpace on 2018-08-01T20:10:46Z (GMT). No. of bitstreams: 1 REX ANTONIO COSTA MEDEIROS - DISSERTAÇÃO PPGEE 2004..pdf: 14601327 bytes, checksum: 5e8b5fae1a59cd77236adc8cc0655c17 (MD5) Previous issue date: 2004-06-22 / CNPq / Nos dias atuais, os sistemas de criptografia e autenticação desempenham um papel fundamental em aplicações que envolvem a manipulação de informações sigilosas, tais como movimentações financeiras, comércio eletrônico, aplicações militares e proteção de arquivos digitais. A popularização do uso dos sistemas de criptografia e autenticação se deve, em grande parte, a descrição de esquema de criptografia por chave pública. A segurança de tais sistemas é baseada na intratabilidade computacional (clássica) de problemas da teoria dos números, como a fatoração em produtos de primos e o problema do logaritmo discreto. A partir da formulação da Mecânica Quântica, foram demonstrados algoritmos que, executados em um computador quântico e consumindo tempo e recursos polinomiais, são capazes de resolver tais problemas. A construção de um computador quântico inviabilizaria, portanto, o uso de sistemas de criptografia e autenticação por chave pública. Nesta dissertação é discutido o problema da autenticação quântica de mensagens clássicas. É proposto um protocolo híbrido que alcança segurança incondicional, mesmo que um criptoanalista disponha de recursos computacionais infinitos, sejam eles clássicos ou quânticos. Através de uma prova matemática formal, é mostrado que o nível de segurança pode ser feito tão alto quanto desejado. Tal segurança é-garantida pelos princípios fundamentais da mecânica quântica. / Nowadays, cryptography and authentication play a central role in applications that manipulates confidential information, like financial transactions, e-commerce, military applications and digital data protection. The explosive growth of cryptosystems is mostly due to the discovery of the so-called public-kcy cryptosystems. The security of such systcms is based on the intractability of some problems from number theory, like factorization and the discrete logarithm problem. After the formulation of the quantum mechanics, several protocols wcre described in order to solve these problems in time and resources polynomials in their argumente. So, one can conclude that public-key cryptosystems are not secure in a scenario where an eavesdropper makes use of quantum computers. In this work it is discussed the problem of quantum authenticating classical messages. It is proposed a non-interactive hybrid protocol reaching information-theoretical security, even when an eavesdropper possesses both infinite quantum and classical computei- power. It is presented a mathematical proof that it is always possible to reach a desirable levei of security. This security is due to the quantum mechanics proprieties of non-orthogonal quantum states.

In this thesis artwork is defined, through analogy with quantum mechanics, as the conjoining of the nonsimultaneously measurable momentum (waves) of artwork-text (words within the primary sources and exhibition catalogues) with the position (particles) of artwork-objects (artist- productivity/exhibition-quantities). Such a proposition allows for the changes within the artwork of the Russian avant-garde to be charted, as such artwork-objects are juxtaposed with different artwork-texts from 1902 to 2009. The artwork of an initial period from 1902 to 1934 is examined using primary-source artwork-text produced by Russian artists and critics in relation to the contemporaneous production-levels of various types of Russian-avant-garde artwork-objects. The primary sources in this dataset are those reproduced in the artwork-text produced by the 62 exhibitions described below, and those published in John E. Bowlt's 1991 edition of Russian Art of the Avant-Garde: Theory and Criticism. The production of artwork in the latter period from 1935 to 2009 is examined through consecutive exhibitions, and the relationship between the artwork-text produced by these exhibitions and the artwork-objects exhibited at them. The exhibitions examined within this thesis are 62 containing Russian avant-garde artwork, held in Britain from 1935 to 2009. Content analysis, using an indices-and-symptom analytical construct, functions to convert the textual, unstructured data of the artwork-text words to numerical, structured data of recording-unit weighted percentages. Whilst artist-productivity and exhibition-quantities of types of artwork-object convert the individual artwork-objects to structured data. Bivariate correlation, descriptive statistics, graphs and charts are used to define and compare relationships between: The recording units of the artwork-texts; the artist-productivity/ exhibition-quantities of types of artwork-objects; the structured artwork-text data and structured artwork-object data. These various correlations between structured artwork-text data and structured artwork-object data are calculated in relationship to time (Years) to chart the changes within these relationships. The changes within these relationships are synonymous with changes within Russian avant-garde artwork as presented from 1902 to 1934 and within the 62 British exhibitions from 1935 to 2009. Bivariate correlations between structured artwork-texts data and structured artwork-objects data express numerically (quantitatively) the ineffable relationships formed over time by large sets of unstructured data in the continued (re)creation of artwork.