This master’s thesis investigates the relationship between supersymmetry and integrability in quantum mechanics. This is done by finding a suitable way to systematically add more supersymmetry to the system. Adding more super- symmetry will give constraints on the potential which will lead to an integrable system. A possible way to explore the integrability of supersymmetric quantum mechanics was introduced in a paper by Crombrugghe and Rittenberg in 1983, their method has been used as well as another approach based on expanding a N = 1 system by introducing complex structures. N = 3 or more supersymmetry is shown to give an integrable system.

The central aim of this thesis is to present a new kind of realism that is driven not from the traditional realism/anti-realism debate but from the practice of physicists. The usual debate focuses on discussions about the truth of theories and how they relate with nature, while the real practices of the scientists are forgotten. The position I shall defend is called "phenomenological realism". The realist doctrine was recently undermined by the argument from pessimistic meta-induction, also known as the argument from scientific revolutions. I argue that phenomenological realism is a new kind of scientific realism that can overcome the problem generated by the pessimistic meta-induction, and which reflects scientific practice. The realist has tried to overcome the pessimistic meta-induction by suggesting various types of theory dichotomy. I claim that the different types of dichotomy normally presented by realists do not overcome the problem, for these dichotomies cut through theory vertically. I argue for a different kind of dichotomy, one that cuts horizontally, between high-level and low-level theoretical representations. I claim that theoretical forms in physics have two distinct types depending on the way they are built. These are theoretical models that are built depending on a top-down approach and phenomenological models that are built depending on a bottom-up approach. I argue that for the most part only phenomenological models are the vehicles of accurate representation. I present two case studies. The first case study is from superconductivity, where I contrast the BCS model of superconductivity with the phenomenological model of Landau and Ginzburg. The other case study is a fresh look at the Bohr-Einstein debate.

The theory of classical chaos is reviewed. From the definition of integrable systems using the Hamilton-Jacobi equation, the theory of perturbed systems is developed and the Kolmogorov-Arnold-Moser (KAM) theorem is explained. It is shown how chaotic motion in Hamiltonian systems is governed by the in tricate connections of stable and unstable invariant manifolds, and how it can be catagorised by algorithmic complexity and symbolic dynamics, giving chaotic measures such as Lyapunov exponents and Kolmogorov entropy. Also reviewed is Gutzwiller's semiclassical trace formula for strongly chaotic systems, torus quantisation for integrable systems, the asymptotic level density for stationary billiards, and random matrix theories for describing spectral fluctuation properties. The classical theory is applied to rotating billiards, particularly the free motion of a particle in a circular billiard rotating uniformly in its own plane about a point on its edge. Numerically, it is shown that the system's classical behaviour ranges from fully chaotic at intermediate energies, to completely integrable at very low and very high energies. It is shown that the strong chaos is due to discontinuities in the Poincare map, caused by trajectories which just glance the boundary-an effect of the curvature of trajectories. Weaker chaos exists due to the usual folding and stretching of the Hamiltonian flow. Approximate invariant curves for integrable motion are found, valid far from the presence of glancing trajectories. The major structures of phase space are investigated: a fixed point and its bifurcation into a two-cycle, and their stabilities. Lyapunov exponents for trajectories are calculated and the chaotic volume for a wide range of energies is measured. Quantum mechanically, the energy spectrum of the system is found numerically. It is shown that at the energies where the classical system is completely integrable the levels do not repel, and at those energies where it is completely chaotic there is strong level repulsion. The nearest neighbour level spacing distributions for various ranges of energy and values of Planck's constant are found. In the semiclassical limit, it is shown that, for energies where the classical system is completely chaotic, the level spacing statistics are Wigner, and where it is completely integrable, the level spacing statistics are Poisson. A model is described for the spacing distributions where the levels can be either Wigner or Poisson, which is useful for showing the transition from one to the other, and ad equately describes the statistics. Theoretically, the asymptotic level density for rotating billiards is calculated, and this is compared with the numerical results with good agreement, after modification of the method to include all levels.

No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1941. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 44).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 139-148).

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-02Bitstream added on 2014-06-13T18:48:13Z : No. of bitstreams: 1 melo_cam_me_ift.pdf: 748344 bytes, checksum: 4ea018751b23b3395fccb8e9c49dc573 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho apresentamos um estudo detalhado da abordagem de Schwinger para a Mecânica Quântica, fazendo sua generalização para sistemas com escalares pertencentes ao conjunto dos quatérnions. Analisamos, em especial, a estrutura da Álgebra de Medida e sua relação com as propriedades físicas observáveis. Estudamos ainda o problema da liberdade de gauge relacionado à quantização do campo eletromagnético livre, e implementamos uma solução alternativa para este problema utilizando o Princípio Variacional de Schwinger, e o campo auxiliar B(x) introduzido por Nakanishi. / In this work we have presented a detailed study of the Schwinger s approach to the Quantum Mechanics, making its generalization for systems with scalars which belong to the quaternion set. In particular, we have analysed the structure of the Algebra of Measurement and its relation with the observable physical properties. We have also studied the problem of the gauge freedom related to the quantization of the free electromagnetic eld and implemented an alternative solution to this one employing the Schwinger s Variational Principle and the B- eld introduced by Nakanishi.

Bell's Theorem demonstrates that factorizable theories for the EPR experiment (EPR) cannot reproduce the quantum correlations. Factorizability is motivated by various locality conditions. So to understand the nature of nonlocality in EPR, we first need to understand the conceptual relations between factorizability, these various locality conditions and the nature of the quantum correlations. That is the main focus of my thesis. My main conclusion is that these conceptual relations are more subtle than the literature has usually suggested. Chapter 1 is a general introduction. In Chapter 2, I review the general framework of factorizable stochastic theories for EPR. I argue that factorizability can be motivated by various locality conditions, even in theories that admit time-dependent states and take the measurement interactions to be neither instantaneous, nor simultaneous. In Chapter 3, I focus on Cartwright' s (1989) and Humphreys' (1989) theories of probabilistic causation for singular events, which are based on modifications of traditional causal linear modelling. I argue (against Cartwright) that local models for EPR in the framework of these theories are committed to factorizability; and so they cannot reproduce the EPR correlations. In Chapter 4, I turn to Stochastic-Einstein Locality (SEL). Hellman (1982) proposed that SEL with some provisos characterizes the No-Superluminal-Action (NSA) of the Special Theory of Relativity (STR), and he argued that SEL is not violated in EPR. Butterfield (1994) proposed that SEL (without Hellman's provisos) characterizes the lack of superluminal Lewisian causation, and he argued that SEL is violated in EPR. I argue that SEL (without Hellman's provisos) is motivated by NSA and spatiotemporal separability. Thus, the violation of SEL might arise from the failure of spatiotemporal separability. And this failure is compatible with NSA and superluminal Lewisian causation. Accordingly, Hellman's and Butterfield's views need not be in tension. In Chapter 5, I focus on the implications for nonlocality of Jarrett's (1984) analysis of factorizability into "locality" and "completeness". I argue that although this analysis cannot distinguish between failures of factorizability which are compatible with STR and those which are not, it is significant for clarifying the implications of Bell's theorem for nonlocality. In Chapter 6, I qmsider three arguments that are intended to deny superluminal causal propagation in EPR, and a fourth argument that is intended to establish the opposite conclusion. I argue that in various ways these arguments have gone wrong. Three of these argument rely on implicit assumptions that have been overlooked. Accordingly, two of them reached a reasonable conclusion, i.e. the failure of separability, for the wrong reasons; whereas the third reached a wrong conclusion, i.e. that the failure of the contiguity of causal processes explains the failure of factorizability in EPR. The fourth relies on a wrong assumption, and thus it reaches a too strong conclusion, that the EPR correlations require superluminal action. My main conclusion is that the quantum correlations require nonseparability . In Chapter 7, I focus on decision theory in the context of EPR. In both EPR and the famous Newcomb's problem (NewProb), there are unscreenable-off correlations. I argue that NewProb can be related to EPR, in the sense that a NewProb can be realized by that experiment.

No description available.

The field of quantum mechanics has revolutionised physics as a subject. Areas such as information theory, computer science and physical sensing have all been affected by the tremendous successes of various quantum protocols. In this thesis I present my contribution to the development of such non-classical protocols. In classical communication theory a message is always carried by physical particles that interact with a transmitter, after which they travel to a receiver. In this thesis I outline a quantum protocol which allows a receiver to obtain a message without receiving any physical object or particles that have interacted with the transmitter-that is, counterfactually. I build my protocol for counterfactual communication on the principles of interaction-free measurements, ensuring that information always propagates in the opposite direction to the protocol particles. The protocol shows how quantum mechanics breaks the previous premise of communication theory. From the perspective of local observers, it is a beautiful manifestation of the non-locality of interaction-free measurements. Furthermore, it is highly robust against experimental errors and external disturbances. The majority of this part of the thesis is based on my published article 'Quantum counterfactual communication without a weak trace' [Phys. Rev. A 94, 062303 (2016)]. Previous to my work, Salih et al. attempted to design a counterfactual communication protocol [Phys. Rev. Lett. 110, 170502 (2013)]. This protocol has been highly controversial. As counterfactual phenomena impose restrictions on the inter-measurement paths of quantum particles, and the physical reality of such paths lacks description in the Copenhagen interpretation of quantum mechanics, an extension of current quantum theory is required to facilitate a discussion. In this thesis I present an operational and interpretation-independent methodology, enabling the discussion of inter-measurement paths of quantum particles. I start by considering the interferometers of counterfactual protocols, making the basic assumption that any quantum evolution naturally involves uncontrolled weak interactions. I then show how the Fisher information of these weak interactions, available at the output of counterfactual experiments, can be used to discuss the pre-measurement past of the particles. Based on this analysis, the protocol developed by Salih et al. is found to strongly violate counterfactuality. However, my protocol is more flexible in that it allows particles to propagate in the opposite direction to the message. This leads to counterfactuality being satisfied-even in the presence of large experimental errors. These results are observed both analytically and numerically. This part of the thesis is based on my article 'Evaluation of counterfactuality in counterfactual communication protocols' [Phys. Rev. A 96, 062316 (2017)]. The numerical methods are inspired by another of my publications: 'Protocol for fermionic positive-operator-valued measures' [Phys. Rev. A 96, 052305 (2017)]. Finally, as the Fisher information measure is found to be useful in evaluating counterfactual protocols, I extend my work by investigating the quantum Fisher information in experiments with general discrete quantum circuits. I prove that the quantum Fisher information of a two-level interaction in a quantum circuit can be expressed by a simple formula. Under certain phase-relations, the formula provides a straightforward connection between the abstract concept of the inter-measurement wavefunction and the quantum Fisher information at the output. With regard to how the information obtained from a certain volume of space influences our perception of classical objects, I argue that the quantum Fisher information measure is highly useful in describing quantum objects. If this measure is applied to observers with a limited set of the experimental measurement outcomes, a quantum object can appear to follow non-classical discontinuous paths. This supports the remarkable conclusion that our perception of the past of a quantum object is subjectively dependent on the measurement we conduct on it.