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Thesis (M.Ed.)--University of the Witwatersrand, Faculty of Education, 1999.

No description available.

Topological insulators (TIs) are a class of quantum materials, which behave as insulators in the bulk, yet possess gapless spin-polarized surface states, which are robust against nonmagnetic impurities. The unique properties of TIs make them attractive not only for studying various fundamental phenomena in condensed matter and particle physics, but also as promising candidates for applications ranging from spintronics to quantum computation. Within the topological insulator realm, a great deal of focus has been placed on discovering new quantum materials, however, ideal multi-modal quantum materials have yet to be found. Here we study alpha-PdBi2, KFe2Te2, and DySb compounds including others within these families with high-resolution angle-resolved photoemission spectroscopy (ARPES) complimented by first principles calculations. We observe unique phase changes and phenomena across their transition temperatures. Our work paves a new direction in material discovery and application related to their unique electronic properties.

<p>Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold.</p> <p>We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques. </p> <p><br></p> <p>With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples.</p> <p>In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local</p> <p>threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model.</p> <p>Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and</p> <p>Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.</p>

This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2n/2n2(log2n)2). This is an improvement over the best known algorithm, with a run time of 2nnO(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can be framed as NP-Hard problems, so any speed-up in the solution of these problems is highly sought after. A bulk of this thesis consists of a review of the underlying principles of quantum mechanics and quantum computing, building to the Quantum Search and Quantum Counting algorithms. The review is written with the assumption that the reader has no prior knowledge on quantum computing. This culminates with a presentation of algorithms for generating the quantum circuits required to solve K-Coloring and Chromatic Number.

One of the major unsolved questions of modern physics is the nature of dark matter, whose existence is inferred from astronomical observations. There are numerous potential dark matter candidates: one strong contender is the axion. The axion was initially proposed to solve the strong CP problem of quantum chromodynamics but it was later realized that its properties make it simultaneously a good candidate for dark matter. Axions couple to the Standard Model in various ways. In this thesis, we describe experiments which exploit the axion coupling gd to the nuclear electric dipole moment (nEDM). In particular, in the presence of an external electric field, the axion perturbs the magnetization of an ensemble of nuclear spins due to this coupling. In the CASPEr-Electric experiment, the axion dark matter interacts with the nuclear spins of 207Pb and the effective electric field is provided by a ferroelectric crystal in which the 207Pb is embedded. CASPEr-Electric is a resonant search where axion dark matter would perturb the equilibrium magnetization of the 207Pb nuclear spin ensemble. The experiment is calibrated through pulsed nuclear magnetic resonance (NMR) experiments on the 207Pb nuclei. The first generation of the experiment demonstrated the feasibility of this method and established limits on the nEDM coupling in the mass range of 162-166 neV (Compton frequency 39-40 MHz). This thesis primarily focuses on the second generation of the CASPEr-Electric experiment, which probed axion dark matter at a lower frequency range of 4 - 5 MHz using superconducting quantum interference devices (SQUIDs). Our search established upper limits on the coupling for axion masses in the range 19.5-20.5 and 21.5-22 neV (4.6 - 5.0 and 5.2 - 5.3 MHz). The upper bound on the nEDM coupling is |gd| < 4 x 10-4, GeV-2 with 95 % confidence. / 2024-11-07T00:00:00Z

Kohn-Sham density functional theory is a rigorous formulation of many-electron quantum mechanics which, for practical purposes, requires approximation of one term in its total energy expression: the exchange-correlation energy. This work elucidates systematic methods for constructing approximations to the exchange-correlation energy solely from first-principles physics. We review the constraints that can be built into approximate density functionals, and use thermochemical data to argue that satisfaction of these constraints permits a more general description of electronic matter. Contact with semiclassical physics is made by studying the turning surfaces of Kohn-Sham potentials in solids. Perfect metals and covalently-bound, narrow-gap insulators do not have turning surfaces at equilibrium, but do under expansive strain. Wide-gap insulators, ionic crystals, and layered solids tend to have turning surfaces at equilibrium. Chemical bonds in solids are classified using the turning surface radii of its constituent atoms. Depletion of the charge density, such as near a monovacancy in platinum, is shown to produce a turning surface. Further, this work demonstrates why generalized gradient approximations (GGAs) are often able to describe some properties of sp-bonded narrow-gap insulators well. A Laplacian-level pure-density functional is developed with the goal of describing metallic condensed matter. This functional is derived from the r2SCAN orbital-dependent meta-GGA, and reduces its tendency to over-magnetize ferromagnets; improves its description of the equation of state properties of alkali metals; and improves its description of intermetallic thermodynamics. It is constructed to enforce the fourth-order exchange gradient expansion constraint (not satisfied by r2SCAN), and a few free parameters are fitted to paradigmatic metallic systems: jellium surfaces and closed-shell jellium clusters. Last, we modify an exchange-correlation kernel that describes the density-density response of jellium to better satisfy known frequency sum rules. We also constrain the kernel to reproduce the correlation energies of jellium, and compare it to a wide variety of common kernels in use for linear response, time-dependent density functional theory calculations. / Physics