Masters Degrees (Physics)

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https://scholar.sun.ac.za/handle/10019.1/3639

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Vacuum contributions to the nucleon energy sum rule
(Stellenbosch : Stellenbosch University, 2024-03) Crowther, Devon Neil; Weigel, Herbert ; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: Within the Nambu Jona-Lasinio(NJL) chiral soliton model nucleon structure functions were previously explored. One of the structure functions, namely the iso-singlet unpolarized nucleon structure function (IUSF), displayed results that did not agree with experimental data. The simulations described in this pa- per aim to investigate this behaviour of the IUSF. The central means of this investigation is the energy sum rule that relates an integral of the IUSF to the mass of the nucleon. Through this investigation, it was dis- covered that the cut-off constant Λ had not been properly computed in that earlier study. This constant is not a numerical parameter but is fully determined by physical constants, such as the pion mass and pion decay constant. Even though the correction was only minor, the adjusted calculation of the IUSF resulted in a significant problem with the sum rule — a numerical inaccuracy that became more apparent at higher grand spins. These inaccuracies in the sum rule become apparent regardless of the Λ value but were signifcantly more so for the corrected Λ. With the validity of our sum rule in numerical jeopardy, an investigation is launched into why this is so and obtaining the appropriate numerical parameters to fix it. Following this, we investigated the deviation from empirical data exhibited by the IUSF. This was done in two ways, first the numerical parameters that encode the discretisation of the quantum fields were changed, secondly the contribution from the non-solitonic background, which defines the reference energy, was changed to better reflect its spatial invariance. In essence a strong dependence of the IUSF on the treatment of the vacuum subtraction was found.
Fourier ptychographic microscopy for high-resolution, large field of view imaging
(Stellenbosch : Stellenbosch University, 2023-12) Fouche, Eugene Egbert; Neethling, Pieter H. ; Bosman, Gurthwin W. ; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: Fourier ptychographic microscopy (FPM) is an imaging technique which overcomes the limitations of conventional microscopy to construct high-resolution, large field of view (FOV) images of a sample. Usually, there is a trade-off between resolution and field of view, but FPM allows samples to be viewed at a high resolution, while maintaining a large FOV. FPM is a computational imaging technique, where multiple low-resolution images of a sample are used to reconstruct the sample at a much higher resolution. The sample is illuminated from various angles, and a low-resolution image is captured for each illumination angle using a lens with a low numerical aperture (NA). The low NA lens has a large FOV, and the various illumination angles allows one to obtain information about the smaller sample features. This allows one to reconstruct a high-resolution, large FOV image of the sample using an iterative reconstruction algorithm. An LED array is typically used to provide the angularly varying illumination. Many real-world samples alter both the amplitude and the phase of the light that is transmitted through them. However, only the intensity can be measured on a camera, and the phase information is lost. In FPM, the various sample images allows one to recover the phase of the sample, as well as the amplitude. This can be used to correct for errors in the imaging setup, and also enhances the contrast when viewing biological samples. In this thesis, the theoretical framework behind FPM is explained, and simulations are performed to investigate the effect of the LED array size and the number of iterations of the reconstruction algorithm on the quality of the reconstructed sample. The error correction (defocus aberration) is also investigated. Two setups are constructed to investigate FPM experimentally. The first setup uses an LED array, and is used to image known calibration targets and real-world biological samples. This setup is also adapted to perform polarization-sensitive FPM (pFPM) on birefringent mineral samples to image the different crystal domains in the samples. The second setup uses a continuous wave laser as the light source and a 2-dimensional spatial light modulator (2D-SLM) to provide the angularly varying illumination. This setup is used to image a known calibration target. Both setups are characterised, and their performance is compared to illustrate their suitability for different imaging scenarios.
A new perspective on Kaluza-Klein theory
(Stellenbosch : Stellenbosch University, 2023-12) Horoto, Langa; Scholtz, Frederik G. ; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: Kaluza-Klein theories are classical theories that unify fundamental forces by treating them as general relativity in more than four spacetime dimensions. The existing theories of this nature make predictions which are not consistent with experiments. In this work, we develop a variant of such theories which is free of all their shortcomings. We achieve this through introduction of a postulate regarding matter and curvature of spacetime which we utilize in con- structing the Lagrangian. The resulting Lagrangian is the simplest Lagrangian respecting all the symmetries of 4D gauge theories and naturally incorporates the Higgs mechanism. However; such a Lagrangian is at odds with the current interpretation of General Relativity. We show that it is this inconsistency of gauge theories and interpretation of general relativity that results in the incor- rect value of the cosmological constant computed from quantum theory. From the equations that follow it is clear that - contrary to the popular assumption- the Ricci flat higher dimensional spacetime can not result in the complete the- ory of fundamental forces. We construct the standard model and show that the minimum number of dimensions of spacetime encompassing all fundamental forces is 16 which is again at variance with other higher dimensional theories. We conclude by showing that the theory does not only results in unification of the fundamental forces but also that of bosons and fermions by demonstrating that spin is a consequence of isometries of spacetime in the same manner that charge is.
Quantum randomness
(Stellenbosch : Stellenbosch University, 2023-03) Strydom, Conrad; Tame, M. S.; Bosman, G. W.; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: Randomness is a vital resource with many important applications in information theory. In particular, random numbers play a ubiquitous role in cryptography, simulation and coordination in computer networks. When ran- domness is generated using classical techniques, the unpredictability relies on incomplete knowledge which can introduce ordered features and compromise the application. This thesis explores the use of quantum techniques to generate true randomness and its application to quantum computing. The analogue of random numbers in quantum information are random unitary operators sampled from the uniform Haar ensemble, which are used in a number of quantum protocols. Unfortunately, these cannot be generated efficiently and so pseudorandom ensembles called unitary t-designs are frequently used as a substitute. In the first part of this thesis we investigate t-designs realised using a measurement-based approach on IBM quantum computers. In particular, we implement an exact single-qubit 3-design on IBM quantum computers by performing measurements on a 6-qubit graph state. We show that the ensemble of unitaries realised was a 1-design, but not a 2-design or a 3-design under the test conditions set, which we show to be a result of depolarising noise. We obtain improved results for the 2-design test by implementing an approximate 2-design, which uses a smaller 5-qubit graph state, but the test still does not pass for all states due to noise. To obtain a theoretical understanding of the effect of noise on t-designs, we investigate the effect of various noise channels on the quality of single-qubit t-designs. We show analytically that the 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4- and 5-design suggest that a 2t-design is significantly more sensitive to noise than a (2t − 1)-design and that, with the exception of amplitude damping, a (2t + 1)-design is as sensitive to noise as a 2t-design. Next, we test our approximate measurement-based 2-design on an important application in quantum com- puting, namely noise estimation. For this, we propose an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement- based gate. We demonstrate our protocol on IBM quantum computers by estimating the fidelity of a universal single-qubit gate set using graph states of up to 31 qubits. Estimated gate fidelities show good agreement with those calculated from process tomography, which shows that our approximate measurement-based 2-design is of sufficient quality for use in randomised benchmarking, despite not passing our test for all states. While IBM quantum computers provide a sophisticated platform for randomness generation, they are not specifically designed for this task. We therefore investigate randomness generation on custom-built hardware, by integrating an on-chip nanowire waveguide into an optical time-of-arrival based quantum random number generation setup. Despite loss, we achieve a random number generation rate of 14.4 Mbits/s. The generated bits did not require any post-processing to pass industry standard tests. Our experiment demonstrates an order of magnitude increase in generation rate and decrease in device size compared to previous studies.
Pinhole interference in three-dimensional fuzzy space
(Stellenbosch : Stellenbosch University, 2023-03) Trinchero, Dario; Scholtz, F. G.; Stellenbosch University. Faculty of Science. Dept. of Physics.
ENGLISH ABSTRACT: We investigate a quantum-to-classical transition which arises naturally within the fuzzy sphere formalism for three-dimensional non-commutative quantum mechanics. We focus on treating a two-pinhole interference configuration within this formalism, as it provides an illustrative toy model for which this transition is readily observed and quantified. Specifi- cally, we demonstrate a suppression of the quantum interference effects for objects passing through the pinholes with sufficiently-high energies or numbers of constituent particles. Our work extends a similar treatment of the double slit experiment, presented in [33], within the two-dimensional Moyal plane, only it addresses two key shortcomings that arise in that context. These are, firstly that the interference pattern in the Moyal plane lacks the expected reflection symmetry present in the pinhole setup, and secondly that the quantum-to-classical transition manifested in the Moyal plane occurs only at unrealistically high velocities and/or particle numbers. Both of these issues are solved in the fuzzy sphere framework.

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