The simulation of the dynamics of quantum systems is very di cult, due to the fact that, in general, it cannot be calculated exactly for interacting many-body systems. Brute force simulations of quantum dynamics are simply not feasible, and approximations need to be made. In many instances a quantum system can be approximated as a quantum-classical system, where only a subsystem of interest is treated quantum mechanically, and the rest is considered as a classical bath. When energy is free to be exchanged between the subsystem and its environment, the dynamics that occur is said to be nonadiabatic. This type of dynamics is challenging to calculate on a computer, as it can lead to large statistical errors at long times. Hence, there is a need for improved algorithms for nonadiabatic dynamics. In this thesis, a recently introduced nonadiabatic sampling scheme [A. Sergi and F. Petruccione, Phys. Rev. E 81, 032101 (2010)] is used to calculate the long-time dynamics of a model system comprising a quantum spin coupled to a bath of harmonic oscillators. Also, various technical aspects of the algorithm are investigated. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

Time variations of the geomagnetic field can be classified into two main categories of internal and external origin with respect to the surface of the Earth. It has been found that the variations that take place on longer time scales (~ 1 year and longer) are commonly known as secular variation (SV) and are of internal origin. There is a need to develop SV models using satellite data as the use of ground data is not always possible with many limitations including the limited data points and lack of data over ocean areas that are not easily accessible. Two regional geomagnetic field modelling techniques namely polynomial surface modelling (PolyM) and Spherical Cap Harmonic Analysis (SCHA) were applied to CHAMP satellite data recorded between 2001 and 2005 to investigate the use of satellite data to develop a geomagnetic SV model over southern Africa. The restricted area of investigation is between 10° and 40° South in latitude and between 10° and 40° East in longitude. The resulting regional models of this investigation were validated against the two widely used global field models IGRF 10 and CHAOS using the available ground survey data obtained during the same period over southern Africa. The results suggest that the regional field models can be derived based entirely on satellite data. However, the regional SV models can be improved by combining both high quality satellite and ground survey data, since they lack the high quality of a global field model like CHAOS. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

A solar thermal energy system is being rebuilt at University of KwaZulu-Natal School of Physics. A similar system is also being built in the University Eduardo Mondlane – Maputo Mozambique, in a team development work. The system is composed mainly of the following subsystems: (i) An Energy capture subsystem: paraboloidal dish concentrator with a heat receiver, mounted on a dual axis polar mount sun tracking assembly; (ii) An Energy storage subsystem: rock-bed thermal energy storage (TES) system; (iii) An Energy utilization subsystem: any user heat utilization (like a cooking or water boiling appliance); and (iv) A monitoring and control subsystem. The subsystem (iv) for performing a controlled charging of the Thermal Energy Storage from a hot plate simulated solar heat, was formerly developed and it was based on 2 conventional data loggers (HP/Agilent) and programs running on 2 PCs. The present work is aimed at performing the same plus additional monitoring and control tasks, based on a low cost microcontroller design. The monitoring and control subsystem based on the Atmel ATmega 32 MCU has been designed and built, capable of performing data acquisition, data logging and control of relevant system variables such as, hour and declination angles of the tracking concentrator; to cite some of the main variables. Besides a huge work of designing, building, programming and testing the microcontroller system itself, a special focus was given to the monitoring and control of the solar heat concentrator, to perform a dual axis sun tracking, so as to get as much as possible of the available solar radiation. Measurements of various system parameters such as, the sun tracking actual hour and declination angles, the inlet and outlet temperatures of both the heat receiver and the rock bed heat storage, etc., for the system under consideration have been carried out. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2009.

Mossbauer Spectroscopy has been used to investigate the site of Fe inclusions in a suite of synthetic diamonds (de Beers MDAS). Information on the hyperfine magnetic fields and electric field gradients at Fe sites in the diamond grains were obtained from Mossbauer Spectroscopy of diamond grains ranging in size from 25 to 250 um. The Fe inclusions in these samples resulted from the synthesis of the diamond grains in which Fe was used as a catalytic solvent. The Mossbauer measurements were carried at room temperature with a constant acceleration spectrometer operating in transmission geometry. The samples with the largest grain size of 180-250 um gave a well defined six component magnetically split spectrum, similar to the Zeeman split sextet obtained for natural iron. As the grain sizes decreased the intensity of the magnetically split components became greatly reduced and a strong paramagnetic component appeared. At grain sizes 105-45 um the spectra are dominated by a central single line with some evidence of an asymmetric doublet. For the finest grain size 38-25 um, the reappearance of the six magnetic hyperfine splitting components together with the strong central single paramagnetic component was observed. The change in the Mossbauer patterns observed with decreasing grain size suggest that a rapid phase transition of the Fe inclusions from ferromagnetic to superparamagnetic takes place. The analysis of Mossbauer spectra yielded a value of the hyperfine magnetic field of Bhf = -32.4(4) T and an electric field gradient in the range of Vzz = 1.4(4) 1.8( 7) X 10'8 V.cm- 2 at the site of the probe s7Fe nucleus. These values compare favourably with other measurements. / Thesis (M.Sc.)-University of Durban-Westville, 1992.

In this thesis a consistent multipole theory is used to describe light propagation in nonabsorbing magnetic cubic and uniaxial crystals to the order of electric octopoles and magnetic quadrupoles. The first chapter extends Maxwell's equations for a vacuum to their macroscopic form in matter by including bound-source contributions as multipole expansions. From these the corresponding forms for D and H are obtained, which ensure origin-independence of Maxwell's equations. A multipole eigenyalue equation describing light propagation in a source-free homogeneous medium is then derived, which is the basic equation applied in this thesis. In the second chapter it is shown how, from the multipolar form of the propagation equation for transverse waves, expressions can be derived for the various birefringences that may be exhibited in macroscopic platelets of the medium, as introduced by Jones in the formulation of his M-matrix. The following chapter presents the derivation, by means of first-order perturbation theory, of the quantum mechanical expressions for the polarizability tensors which enter the eigenvalue wave equation. The origin independence of the expressions for the various observable quantities is then established. In the fourth chapter the independent components of the polarizability tensors are calculated for two selected crystal point groups, namely 622 and 432, by way of illustration. In chapter five the components calculated in the manner illustrated in the previous chapter are presented in tabular form. The Jones method outlined in chapter two is then applied to the crystal point group 6m2, again as an illustration of the method used to determine the optical effects displayed by this point group. Chapter five concludes with a table containing a listing of the predicted optical effects calculated in this way for all of the magnetic uniaxial and cubic point groups. The thesis concludes with chapter six, in which a summary of the results of the work undertaken is given, together with a discussion of factors influencing measurements of the predicted optical effects. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1997.

This dissertation deals with theory and algorithms for computer simulations of classical and quantum systems in the canonical ensemble. First, the approach of Nos e-Hoover and its generalization, known as the Nos e- Hoover chain dynamics, are introduced. Such methods are used in classical molecular dynamics simulations to control the temperature of particle systems through a coupling to a few additional fictitious variables, mimicking an in nite thermal reservoir. In order to introduce the extension of the Nos e-Hoover method to quantum systems, the features of the Wigner representation of quantum mechanics are reviewed. Finally, a recent approach [A. Sergi and F. Petruccione, J. Phys. A 41 355304 (2008)], which extends the Nos e-Hoover and Nos e-Hoover chain equations in quantum phase space, is described. Such a method is applied to a single harmonic mode, and the conditions for quantum-to-classical transitions as a function of the thermodynamical temperature are studied by means of numerical simulations. It is shown that, in the case of strong coupling, the open system dynamics simulated by Nos e-Hoover chain equations leads to quantum-classical transition of the Wigner function of the harmonic mode. Agreement between the numerical and analytical results is also found. The algorithms and results illustrated are of interest to the numerical simulation of the quantum dissipative dynamics of more general systems. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

In this dissertation, we consider the variable chaplygin gas (VCG) model as derived from the Tachyon gas model and search for a sub-class of models that provide an adequate fit to the cosmic microwave background (CMB) observations. We find that, for an appropriate choice of VCG parameters, up to ~ 80% of the VCG collapses into a gravitationally bound condensate which behaves as matter; the evolution of the remaining VCG, as governed by its equation of state, brings about accelerated expansion at late times. In light of this high collapsed fraction, we approximate the VCG transfer function with that of cold dark matter. We show that we can sufficiently describe the VCG cosmology from decoupling to today in terms of a model in which the gravitationally bound condensate plays the role of cold dark matter and the remaining VCG takes the place of dark energy in the concordance model. We then compute the CMB temperature anisotropy spectrum for a subset of VCG models and proceed to find a best-fit model to the WMAP-9yr data [46]. Our best-fit model has a x² per degrees of freedom of 2.03. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Standard quantum computation proceeds via the unitary evolution of physical qubits (two-level systems) that carry the information. A remarkably different model is one-way quantum computing where a quantum algorithm is implemented by a set of irreversible measurements on a large array of entangled qubits,, known as the cluster state. The order and sequence of these measurements allow for different algorithms to be implemented. With a large enough cluster state and a method in which to perform single-qubit measurements the desired computation can be realised. We propose a potential implementation of one-way quantum computing using qubits encoded in the orbital angular momentum degree of freedom of single photons. Photons are good carriers of quantum information because of their weak interaction with the environment and the orbital angular momentum of single photons offers access to an infinite-dimensional Hilbert space for encoding information. Spontaneous parametric down-conversion is combined with a series of optical elements to generate a four-photon orbital angular momentum entangled cluster state and single-qubit measurements are carried out by means of digital holography. The proposed set-up, which is based on an experiment that utilised polarised photons, can be used to realise Grover’s search algorithm which performs a search through an unstructured database of four elements. Our application is restricted to a two-dimensional subspace of a multi-dimensional system, but this research facilitates the use of orbital angular momentum qubits for quantum information processing and points towards the usage of photonic qudits (multi-level systems). We also review the application of Dirac notation to paraxial light beams on a classical and quantum level. This formalism is generally employed in quantum mechanics but the analogy with paraxial optics allows us to represent the classical states of light by means of Dirac kets. An analysis of the analogy between the classical and quantum states of light using this formalism, is presented. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.

Various strategies have been tested for obtaining integrated intensities from x-ray powder diffractometer data. An asymmetric pseudo-Voigt profile function was used to fit the pattern in the region above 2θ = 35̊ (Cu-Kα radiation). At lower angles where the asymmetry was strongest and the profile function not suitable the peaks were integrated numerically. A smooth background function was estimated from the regions of minimum intensity of the pattern. The profile parameters were initially refined in small ranges of about 10̊ 2θ in order to determine their 2θ-dependence. Thereafter final refinements of peak intensities were undertaken using the profile parameters thus determined. Analysis of data from the mineral Fe-akermanite, Ca₂Mg₀. ₄Fe₀. δSi₂O₇, generated 173 integrated intensities with 1 > 2δ(1) out of 187 positions separated in 2θ by more than 0,02̊. Of the total of 213 reflections in the range, those overlapping exactly or separated by < 0,02̊ were treated as single peaks. The structure was refined using an overall isotropic temperature parameter and a parameter to compensate for preferred orientation, giving an unweighted residual of 10,4% for 14 parameters. / Thesis (M.Sc.)-University of Durban-Westville, 1988.

The interaction of an anisotropic (in velocity space) ion beam with an isotropic background hydrogen plasma is theoretically investigated. The length and time scales are such that both the ions and electrons are magnetized. Using linear theory, the electrostatic dispersion relation is derived, and solved fully, using no approximations. It is shown that the anisotropy can significantly enhance the instability growth rates as compared to the isotropic case. The importance of ion magnetization is illustrated. Comparisons are made with unmagnetized plasma results. The modulational instability of an arbitrarily-large-amplitude electron cyclotron wave along the external magnetic field is investigated, taking into account the relativistic electron quiver velocity and the relativistic ponderomotive force. Three types of plasma slow responses, the forced-Raman, quasistatic and forced-quasistatic, are considered and a parameter study of the instability growth rates is carried out. / Thesis (M.Sc.)-University of Durban-Westville, 1989.