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In this thesis I address two different topics in quantum theory. The first one is the long discussed Schrodinger's cat problem, and the issues related to having a macroscopic superposition state. I show that the quantum theory provides full explanation to the problem. In the second part, I discuss the time measurement related issues in quantum mechanics. Since there does not exist any time operator in quantum mechanics generally, time is not directly measurable. Therefore we should devise other methods to register time. We study different time-energy relations and will find that accurate clocks have high energy uncertainties. If we use accurate clocks in quantum systems to observe their time evolutions, their high energy uncertainties interfere with system's normal evolution and slows it down. I also provide a formal proof to a previously suggested limiting accuracy relation on the measurements of the time-of-arrival experiments. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This dissertation is ordered into three Parts. Part I is an investigation into identity, indiscernibility and individuality in logic and metaphysics. In Chapter 2, I investigate identity and discernibility in classical first-order logic. My aim will will be to define four different ways in which objects can be discerned from one another, and to relate these definitions: (i) to the idea of symmetry; and (ii) to the idea of individuality. In Chapter 3, the four kinds of discernibility are put to use in defining four rival metaphysical theses about indiscernibility and individuality. Part II sets up a philosophical framework for the work of Part III. In Chapter 4, I give an account of the rational reconstruction of concepts, inspired chiefly by Carnap and Haslanger. I also offer an account of the interpretation of physical theories. In Chapter 5, I turn to the specific problem of finding candidate concepts of particle. I present five desiderata that any putative explication ought to satisfy, in order that the proposed concept is a concept of particle at all. Part III surveys three rival proposals for the concept of particle in quantum mechanics. In Chapter 6, I define factorism and distinguish it from haecceitism. I then propose an amendment to recent work by Saunders, Muller and Seevinck, which seeks to show that factorist particles are all at least weakly discernible. I then present reasons for rejecting factorism. In Chapter 7, I investigate and build on recent heterodox proposals by Ghirardi, Marinatto and Weber about the most natural concept of entanglement, and by Zanardi about the idea of a natural decomposition of an assembly. In Chapter 8, I appraise the first of my two heterodox proposals for the concept of particle, varietism. I define varietism, and then compare its performance against the desiderata laid out in Chapter 5. I argue that, despite its many merits, varietism suffers a fatal ambiguity problem. In Chapter 9, I present the second heterodox proposal: emergentism. I argue that emergentism provides the best concept of particle, but that it is does so imperfectly; so there may be no concept of particle to be had in quantum mechanics. If emergentism is true, then particles are (higher-order) properties of the assembly, itself treated as the basic bearer of properties.

The scope of work in this dissertation has comprised several major investigations on applications and theoretical studies of ab initio quantum mechanics and density functional theory where those techniques were applied to the following: (i) investigation of the performance of density functionals for the computations of molecular properties of 3d transition metal containing systems; (ii) guidance for experimental groups for rational design of macrometallocyclic multinuclear complexes with superior π-acidity and π-basicity that are most suitable for p- and n-type semiconductors of metal-organic molecules and nanomaterials; (iii) investigation of the metallo-aromaticity of multi-nuclear metal complexes; (iv) investigation of the kinetics and thermodynamics of copper-mediated nitrene insertion into C-H and H-H bond; and (v) accurate computations of dissociation energies of hydrogen-bonded DNA duplex moieties utilizing the resolution of identity correlation consistent composite approach (RI-ccCA).

The main objective of the thesis is to carry out structural bioinformatics study along with usage of advanced quantum chemical methods to look at the structural stability and energetics of RNA building blocks. The main focus of the work described here lies on understanding the reasons behind the intrinsic stability of key interactions in nucleic acids. Crystal structures of RNA molecules exhibit fascinating variety of non-covalent interactions, which play an important role in maintaining the three dimensional structures. An accurate atomic level description of these interactions in the structural building blocks of RNA is a key to understand the structure-function relationship in these molecules. An effort has been made to link the conclusions drawn from quantum chemical computations on RNA base pairs in wide biochemical context of their occurrence in RNA structures. The initial attention was on the impact of natural and non-natural modifications of the nucleic acid bases on the structure and stability of base pairs that they are involved in. In the remaining sections we cover other molecular interactions shaping nucleic acids, as the interaction between ribose and the bases, and the fluoride sensing riboswitch system in order to investigate structure and dynamics of nucleic acids at the atomic level and to gain insight into the physical chemistry behind.

The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with such a treatment of probability.

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Les phénomènes de groupe ont été utilisés depuis l'antiquité dans différents domaines comme la thérapie, le social, l'économie et la politique. Selon Bion, les interactions entre les membres d'un groupe génèrent un « inconscient groupal » et son comportement est gouverné et orienté pas les « Hypothèse de base » de Bion. Ce travail a été mené pendant une formation d'analyse de groupe à la Fondation Basque pour les Investigations en Santé Mentale (OMIE) à Bilbao, sur onze sessions. Les participants ont rempli un « questionnaire absurde » avec 50 paires d'images, dont il fallait en choisir une de chaque paire. Les résultats ont été élaborés dans le but de chercher, à travers l'amplification de l'inconscient, une possible influence de la dynamique groupale sur les choix des images des questionnaires. Nos analyses ont trouvé une évidence significative en faveur d'un effet de la dynamique groupale sur les choix initiaux des images, mais aussi sur l'évolution du nombre des changements (swaps) des images choisies au long des onze sessions. Nous avons aussi trouvé des relations entre les orientations des réponses dans les différents groupes, en tant que résultats d'Analyse en Composantes Multiples et du calcul de l'Entropie de la distribution de Bernoulli. Nous interprétons ces corrélations comme des effets groupaux à la lumière de la théorie groupale de Bion, qui postule une orientation inconsciente immédiate du groupe et son évolution successive tout au long des activités groupales.Mots clés : Dynamique de Groupe, Amplification de l'Inconscient, Model Quantique, Entropie / Group phenomena have been used since antiquity in therapeutic, social, economic and political domains. According to Bion, the interactions between group members generate a “group unconscious” and its behaviour is governed and oriented by Bion's “basic assumptions.” The present work has been conducted during group analysis training at the Basque Foundation for the Investigation of Mental Health (OMIE) at Bilbao, consisting of eleven sessions. The participants are presented with an “absurd questionnaire” proposing 50 pairs of images, in each of which one image has to be chosen. The results are used to search through an unconscious amplification for evidence in favour of the influence of group dynamics on individual choices of the images proposed in the questionnaire. Our analysis finds some significant evidence for an effect of group dynamics both on the initial choice of the pictures and on the evolution of the number of changes (swaps) of picture choices across the eleven sessions. We find also some relations between the orientation of the answers in the groups as results of Multiple Variable Analysis and calculation of the distribution of Bernoulli's Entropy. We interpret these correlations as group effects in the light of Bion's view of group dynamics, which postulates an immediate onset of a group unconscious and its evolution during the group activity.Keywords: Group Dynamics, Unconscious Amplification, Quantic Model, Entropy

The introduction of supersymmetry has led to great progress in the study of quantum field theories. Notably, with supersymmetry, properties of a quantum field theory can be computed with higher precision than what would otherwise be possible. In this project, we investigate supersymmetry in the context of quantum mechanics. In particular, we show how the Witten index is insensitive to the details of the supersymmetric quantum mechanical system, making it a robust quantity when considering variations in the system’s parameters. Explicit calculations of the supersymmetric ground states are carried out to identify what determines the Witten index. The concept of superpotential is introduced and we relate Morse theory to the Witten index by identifying the superpotential as a Morse function. Moreover, we consider supersymmetric quantum mechanics on compact orientable Riemann manifolds. We show how the structure of supersymmetric quantum mechanics has a close connection to topological properties of the target manifolds. Specifically, the Witten index is shown to be the Euler characteristic, a topological invariant.

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