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Bound states for A-body nuclear systemsMukeru, Bahati 03 1900 (has links)
In this work we calculate the binding energies and root-mean-square radii for A−body
nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ
the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic
potentials. The equations are solved numerically. For this purpose, the equations are
transformed into an eigenvalue equation via the orthogonal collocation procedure using
triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted
Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined.
For A > 3, the Potential Harmonic Expansion Method is employed. Using this method,
the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike
amplitudes are expanded on the potential harmonic basis. To transform the resulting
coupled differential equations into an eigenvalue equation, we employ again the orthogonal
collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding
eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground
state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O
and 40Ca. / Physics / M. Sc. (Physics)
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Mécanique quantique supersymétrique et opérateurs d’échelle pour le système de Rosen-MorseGarneau-Desroches, Simon 07 1900 (has links)
Le présent mémoire est dédié à l’étude du rôle de la mécanique quantique supersymétrique dans la construction d’opérateurs d’échelle et de leurs applications pour le système quantique de Rosen-Morse. L’aboutissement de ces travaux est contenu dans un article qui constitue le dernier chapitre du mémoire. Précisément, on motive l’échec de la réalisation des opérateurs d’échelle comme opérateurs différentiels pour le potentiel de Rosen-Morse avec les méthodes traditionnelles. On exploite la propriété d’invariance de forme dans le contexte de la mécanique quantique supersymétrique comme un outil alternatif pour offrir une première approche quantique à la réalisation des opérateurs d’échelle pour la version hyperbolique de ce potentiel. On utilise cette réalisation pour obtenir celle d’opérateurs d’échelle pour une classe particulière d’extensions rationnelles du potentiel de Rosen-Morse hyperbolique avec des techniques issues de la supersymétrie. Des états cohérents sont construits à partir des réalisations obtenues pour les différents systèmes. Certaines de leurs propriétés sont analysées et mises en comparaison. En parallèle, on utilise une transformation canonique ponctuelle pour déduire une première réalisation des opérateurs d’échelle comme opérateurs différentiels pour le système de Rosen-Morse trigonométrique. De cette réalisation sont construits des états cohérents pour lesquels des propriétés sont similairement analysées. / This master thesis is dedicated to the study of the role of supersymmetric quantum mechanics in the construction of ladder operators and of their applications for the quantum Rosen-Morse system. The results of this work are presented in an article that constitutes the last chapter of the thesis. Precisely, we motivate the failure of traditional methods in providing a realization for the Rosen-Morse ladder operators as differential operators. We provide a first quantum-based solution to this problem by using the shape invariance property in supersymmetric quantum mechanics as a tool in the construction of the ladder operators for the hyperbolic version of this potential. We use the latter realization to obtain that of a specific class of rational extensions of the hyperbolic Rosen-Morse system by means of supersymmetric techniques. Coherent states are constructed from the ladder operators obtained for the different systems. Some properties are analyzed and compared. In addition, we make use of a point canonical transformation in the derivation of the first realization of the ladder operators of the trigonometric Rosen-Morse system as differential operators. From this realization, we construct coherent states for which some properties are similarly analyzed.
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An investigation of parity and time-reversal symmetry breaking in tight-binding latticesScott, Derek Douglas January 2014 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits.
Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides.
In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold.
In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.
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Aspects of Non-Equilibrium Behavior in Isolated Quantum SystemsHeveling, Robin 06 September 2022 (has links)
Based on the publications [P1–P6], the cumulative dissertation at hand addresses quite diverse
aspects of non-equilibrium behavior in isolated quantum systems. The works presented in
publications [P1, P2] concern the issue of finding generally valid upper bounds on equilibration
times, which ensure the eventual occurrence of equilibration in isolated quantum systems. Recently,
a particularly compelling bound for physically relevant observables has been proposed. Said
bound is examined analytically as well as numerically. It is found that the bound fails to give
meaningful results in a number of standard physical scenarios. Continuing, publication [P4]
examines a particular integral fluctuation theorem (IFT) for the total entropy production of a
small system coupled to a substantially larger but finite bath. While said IFT is known to hold
for canonical states, it is shown to be valid for microcanonical and even pure energy eigenstates
as well by invoking the physically natural conditions of “stiffness” and “smoothness” of transition
probabilities. The validity of the IFT and the existence of stiffness and smoothness are numerically
investigated for various lattice models. Furthermore, this dissertation puts emphasis on the issue
of the route to equilibrium, i.e., to explain the omnipresence of certain relaxation dynamics in
nature, while other, more exotic relaxation patterns are practically never observed, even though
they are a priori not disfavored by the microscopic laws of motion. Regarding this question, the
existence of stability in a larger class of dynamics consisting of exponentially damped oscillations
is corroborated in publication [P6]. In the same vein, existing theories on the ubiquity of certain
dynamics are numerically scrutinized in publication [P3]. Finally, in publication [P5], the recently
proposed “universal operator growth hypothesis”, which characterizes the complexity growth of
operators during unitary time evolution, is numerically probed for various spin-based systems in
the thermodynamic limit. The hypothesis is found to be valid within the limits of the numerical
approach.
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Analogue Hawking radiation as a logarithmic quantum catastropheFarrell, Liam January 2021 (has links)
Masters thesis of Liam Farrell, under the supervision of Dr. Duncan O'Dell. Successfully defended on August 26, 2021. / Caustics are regions created by the natural focusing of waves. Some examples include rainbows, spherical aberration, and sonic booms. The intensity of a caustic is singular in the classical ray theory, but can be smoothed out by taking into account the interference of waves. Caustics are generic in nature and are universally described by the mathematical theory known as catastrophe theory, which has successfully been applied to physically describe a wide variety of phenomena. Interestingly, caustics can exist in quantum mechanical systems in the form of phase singularities. Since phase is such a central concept in wave theory, this heralds the breakdown of the wave description of quantum mechanics and is in fact an example of a quantum catastrophe. Similarly to classical catastrophes, quantum catastrophes require some previously ignored property or degree of freedom to be taken into account in order to smooth the phase divergence. Different forms of spontaneous pair-production appear to suffer logarithmic phase singularities, specifically Hawking radiation from gravitational black holes. This is known as the trans-Planckian problem. We will investigate Hawking radiation formed in an analogue black hole consisting of a flowing ultra-cold Bose-Einstein condensate. By moving from an approximate hydrodynamical continuum description to a quantum mechanical discrete theory, the phase singularity is cured. We describe this process, and make connections to a new theory of logarithmic catastrophes. We show that our analogue Hawking radiation is mathematically described by a logarithmic Airy catastrophe, which further establishes the plausibility of pair-production being a quantum catastrophe / Thesis / Master of Science (MSc)
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Unraveling Walt WhitmanCristo, George Constantine 18 May 2007 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / Explores Walt Whitman's use of Thomas Carlyle's language of textiles, as well as the relation of this language to modern science.
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Computational Modeling of Cancer-Related Mutations in DNA Repair Enzymes Using Molecular Dynamics and Quantum Mechanics/Molecular MechanicsLeddin, Emmett Michael 05 1900 (has links)
This dissertation details the use of computational methods to understand the effect that cancer-related mutations have on proteins that complex with nucleic acids. Firstly, we perform molecular dynamics (MD) simulations of various mutations in DNA polymerase κ (pol κ). Through an experimental collaboration, we classify the mutations as more or less active than the wild type complex, depending upon the incoming nucleotide triphosphate. From these classifications we use quantum mechanics/molecular mechanics (QM/MM) to explore the reaction mechanism. Preliminary analysis points to a novel method for nucleotide addition in pol κ. Secondly, we study the ten-eleven translocation 2 (TET2) enzyme in various contexts. We find that the identities of both the substrate and complementary strands (or lack thereof) are crucial for maintaining the complex structure. Separately, we find that point mutations within the protein can affect structural features throughout the complex, only at distal sites, or only within the active site. The mutation's position within the complex alone is not indicative of its impact. Thirdly, we share a new method that combines direct coupling analysis and MD to predict potential rescue mutations using poly(ADP-ribose) polymerase 1 as a model enzyme. Fourthly, we perform MD simulations of mutations in the protection of telomeres 1 (POT1) enzyme. The investigated variants modify the POT1-ssDNA complex dynamics and protein—DNA interactions. Fifthly, we investigate the incorporation of remdesivir and other nucleotide analogue prodrugs into the protein-RNA complex of severe acute respiratory syndrome-coronavirus 2 RNA-dependent RNA polymerase. We find evidence for destabilization throughout the complex and differences in inter-subunit communication for most of the incorporation patterns studied. Finally, we share a method for determining a minimum active region for QM/MM simulations. The method is validated using 4-oxalocrotonate, TET2, and DNA polymerase λ as test cases.
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Quantum Error Correction in Quantum Field Theory and GravityKeiichiro Furuya (16534464) 18 July 2023 (has links)
<p>Holographic duality as a rigorous approach to quantum gravity claims that a quantum gravitational system is exactly equal to a quantum theory without gravity in lower spacetime dimensions living on the boundary of the quantum gravitational system. The duality maps key questions about the emergence of spacetime to questions on the non-gravitational boundary system that are accessible to us theoretically and experimentally. Recently, various aspects of quantum information theory on the boundary theory have been found to be dual to the geometric aspects of the bulk theory. In this thesis, we study the exact and approximate quantum error corrections (QEC) in a general quantum system (von Neumann algebras) focused on QFT and gravity. Moreover, we study entanglement theory in the presence of conserved charges in QFT and the multiparameter multistate generalization of quantum relative entropy.</p>
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Charge Transport in Nano-Constrictions and Magnetic MicrostructuresTolley, Robert Douglas 10 August 2012 (has links)
No description available.
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Population dynamics of hybrid ecosystems: Implications for marginal ecosystem conservation and managementNichter, Ashlee N. 29 November 2017 (has links)
No description available.
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