The purpose of this dissertation is to review the salient features of non-Hermitian quantum mechanics. An introduction to Hermitian quantum mechanics is included to make this review as accessible as possible. Attempts at formulating a consistent physical theory are introduced, before examining non-Hermitian theories' uses as convenient computational frameworks. Particular emphasis is placed on recent developments in open quantum systems that utilise non-Hermitian Hamiltonians. Chapter four introduces a logic that maps a non-Hermitian Hamiltonian onto a non-Hamiltonian algebra that has a Hermitian Hamiltonian. This was put forward by Sergi, who then goes on to show its application to a two level system. The time evolution is then derived in terms of the density matrix model. This system can then be used to analyse di erent types of decay such as coherence and population di erence. This serves to illustrate the usefulness of the approach. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

No abstract available. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2004.

Amorphous metallic alloys are produced by a variety of techniques some of which involve rapid solidification of the alloying constituents. In these methods the solidification occurs so rapidly that the atoms are frozen-in and partially retain their liquid configuration. There are clear structural and other indications from their various properties that amorphous metallic alloys possess short range order but lack long range order. In general, amorphous alloys are not in a thermodynamic equilibrium state and, therefore, relax structurally whenever atoms attain an appreciable mobility. Associated with structural relaxation, many physical properties change; some significantly and others only slightly. Relaxation experiments in amorphous metallic alloys often display approximate In(t) kinetics which can be understood in terms of various models. In the present work the model by Primak (1955), for which the kinetic behaviour of a system depends on processes that are distributed over a range of activation energies, is used as a basis for further development. The Primak model allows, in principle, for the identification of the order of the relaxation reaction and for the determination of an initial activation energy spectrum Po(Єo), where Єo is a characteristic activation energy. Although the model provides for a qualitative explanation of the In(t) law, it has no predictive power as to the quantitative changes accompanying the various relaxing properties. Furthermore, an estimation of Po( Єo), inferred from various isothermal annealing procedures, reveals the approximate shape but does not fix its location on the activation energy axis. These shortfalls are attributed to complications in the frequency factor v, inherent to the Primak model. Also, the Primak model does not include consideration of the entropy involved in a 'configurational jump' of any particular atom during the relaxation process. Inclusion of the configurational entropy through the frequency factor v, in the present treatment, leads to a 'relaxation equation'. Structural relaxation measurements of density (in practice length - from which density can be approximately inferred) and electrical resistivity, in an Fe4oNi40B20 alloy, have been obtained and fitted to this relaxation equation. The fitting parameters are found, within experimental error, to be the same for both length and resistivity relaxation. The initial activation energy spectrum Po(Єo), as inferred from the fits, over the energy range 1.4 to 2.0 eV, reveals roughly three regimes, namely below 1.5 eV, from 1.5 to 1.8 eV, and above 1.8 eV, respectively, over which the initial activation energy spectrum Po( Єo) assumes different approximately constant values. Previous treatments have, however, implicitly assumed that Po( Єo) is constant throughout a temperature range over which In(t) kinetics is observed. The behaviour observed in this work is associated with the intrinsic relaxation mechanism involving consecutive diffusion of the metallic and metalloid atoms, respectively. A configurational entropy change inferred from this work is found to be negative as a consequence of contraction of the spread-out free volume resulting from thermal fluctuations. Within the framework of the 'present model', other related behaviour of amorphous metallic alloys, including the glass transition, crystallization and diffusion, are discussed. Where direct comparison between theory and experiment is possible for the various observed phenomena, the agreement is good and shows an overall consistency in our approach. Finally, the analysis considered here gives an expression which can be easily used to make quantitative predictions about the experimental relaxation behaviour. An immediate understanding of some of the main features of experimental data on relaxation can, therefore, be obtained through application of the present model. / Thesis (Ph.D.)-University of Natal, Durban, 1998.

Recent high-pressure experiments on iridium show a transition to a 14 atomic layer superlattice structure. Since iridium has a high bulk modulus, it is used in many high-pressure applications, for instance as a gasket for high-temperature, high-pressure diamond anvil cell experiments. The effects of pressure on this material are hence of interest. Of the transition metals, the iridium surface has been one of the most extensively studied surfaces experimentally. The field ion microscope has made it possible to observe in detail the behaviour of adatoms on the surface, and has led to interesting discoveries of the nature of atomic adsorption on the lr(111) surface. A number of theoretical and semi-empirical studies have been made on this topic. However, none of these studies take atomic relaxations into account in a satisfactory manner, and therefore do not give a complete understanding of the process of incorporation of adatoms onto the surface. In the present work, first-principles total energy calculations based on the plane wave pseudopotential method within the framework of the density functional theory are employed in the study of the bulk properties of iridium, and the crystal phases and defect structures of iridium under pressure. The bond-orientation model is extended to include the effects of pressure, and used to compute all of the ~2n defect structures of iridium as a function of atomic volume. Allowance for full atomic relaxations is made in computing the ideal and relaxed surface formation energies of the three low-index surfaces of iridium, and in investigating the nature of adsorption of single adatoms on the lr(111) surface. The formation energy of a vacancy on the Ir(111) surface is also computed. This is the first time such a calculation has been made. / Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 2003.

This thesis represents the development and evaluation of a theory for sound transmission analysis by sound intensimetry. In the context of this study sound transmission analysis is understood to embrace the following: (1) The measurement of sound reduction indices. (2) Diagnostic analysis of sound transmission through panels and structures. The sound intensity method is examined against the theoretical background of the classic two-room method which forms the basis of currently used international standards. The flanking problem, which is one of the principle limiting factors in the use of the classic method, is analyzed. The standard formulation of the intensity method is expanded to account for leakage error, boundary interference effects and calibration mismatch. It is shown that the commonly observed low-frequency discrepancy between intensity and classic method results is resolved by application of the Waterhouse correction. Sound absorption by the test object on the receiving side is shown to cause an error which increases with the flanking factor and with the fraction of the receiving room absorption located on the surface of the test object. Guidelines are developed for the assessment and control of absorption error in practical situations. Using the common mode rejection index as a performance rating for sound intensity meters, the measurement of sound transmission in reactive fields is investigated. Derivation of a formula for the reactivity near the surface of a transmitting panel surrounded by a flanking structure in a reverberant field, leads to the development of a theoretical framework and criteria for the planning and evaluation of test arrangements for sound transmission analysis. Guidelines are given for the calculation of minimum receiving room absorption and the microphone spacing required in practical situations. A study of the characteristic properties of sound intensity fields in diffuse and non-diffuse environments is used as a basis in formulating a new method of measuring directional diffusivity. Based on the relationship between reactivity and the degree of directional balance in a sound intensity field, this method involves spatial averaging of the pressure level and determination of the magnitude of the total intensity vector at the point under consideration. A direct-reading diffusivity meter has been developed and employed in assessing diffusivity in practical situations. The effect of a lack of directional diffusivity on the accuracy of sound transmission analysis in reactive fields is examined. Criteria for calculating minimum diffusivity requirements in the source and receiving room are developed and evaluated experimentally. / Thesis (Ph.D.)-University of Natal, 1985.

Determining the electric quadrupole moments of gas molecules from measurements of birefringence induced in the gas by an applied electric field gradient is widely recognised as being the most direct experimental technique for this purpose. This thesis presents a new molecular theory of the experiment, and also describes the apparatus used in the measurement of the quadrupole moments of a number of gases and the revisions made to the manner in which the experiment was performed. A recent eigenvalue theory of light propagation in matter has been used to derive an expression relating the induced birefringence to the electric quadrupole moment of the molecule, whether this be dipolar or not. This expression is different from that which has previously been applied to dipolar molecules. It is shown that the new expression is independent of molecular origin only if it is cast in terms of the primitive quadrupole moment, as opposed to the traceless moment. Previous work using the same set of apparatus yielded results for carbon dioxide which were significantly lower than those reported by other workers. By using the Jones calculus to re-examine the cascade of optical components used in the experiment, it was found that the previous method of performing the experiment did not completely eliminate the effects of an imperfect retardance in the quarter-wave plate used, nor of strain-induced birefringence in the windows of the the cell containing the gas. These effects could cause results to be underestimated by as much as 8%. It is shown that a better method of performing the experiment is to amplify the optical signal by deliberately offsetting the analysing prism, rather than the quarter-wave plate as was previously done. The results of measurements made using this technique are reported for carbon dioxide, carbon monoxide, nitrogen, ethene, chlorine, and boron trifluoride. The measured quadrupole moment of carbon dioxide is in good agreement with the most recent values found by other workers using a similar experiment, and with the latest theoretical value of this quantity. / Thesis (PH.D.)-University of Natal, Pietermaritzburg, 1993.

Ab initio plane wave based density functional calculations within the generalised gradient approximation (GGA) have been carried out on a wide range of phases and stoichiometries for the platinum-titanium (Pt-Ti) and iridium-titanium (Ir-Ti) alloy systems, using the Vienna Ab Initio Simulation Package (VASP) with projector augmented wave (PAW) potentials. For all of the phases in this work, the equilibrium structures were found by performing a full relaxation of the atoms. There were 20 di erent phases considered for varying atomic percentage compositions for each alloy system. Energy-volume calculations and heats of formations were used to determined the equilibrium structures at each atomice percentage composition and to determine if there were high temperature phases at that composition. The elastic constants and elastic moduli are calculated and the electronic structure and density of states (DOS) were considered to understand the hardness and stability properties of the alloys. For the Pt-Ti system, the low and high temperature phases at di erent compositions agreed with previously published results in the literature. Intermediate phases at 50% were also determined, in agreement with previous results. Alloying Pt with Ti resulted in a decrease in the bulk modulus, i.e. not adding strength to the metal. However, the shear modulus increased for most of the alloys compared to bulk Pt and it was found that in general, alloying may increase the resistance to shear. PtTi alloys were found to be ductile in nature, as with both constituent metals in their bulk form. In the Ir-Ti system, bulk Ir was found to have the highest bulk, shear and Young's modulus with each of these values decreasing with increasing percentage Ti in the alloy. IrTi alloys with 66.7% Ir composition or higher were found to be brittle in nature, similar in behaviour to bulk Ir; alloys with a higher percentage concentration of Ti were found to be ductile. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

III-V compound semiconductors such as Gallium Arsenide, Indium Phosphide as well as Indium Arsenide have recently demonstrated the capability of applications in high speed semiconductor devices compared to those made from Silicon. As a result, III-V compound semiconductors have drawn attention of material researchers, in particular in understanding the effects that may occur during manufacturing of these devices. Optical and electrical properties of a device may alter when a foreign atom is introduced during the manufacturing of the device. However, the foreign atom may also lead to the formation of lattice disorder (defects). A convenient way of introducing impurity atoms into a substrate and tailoring their functionality for particular applications is by ion implantation. Mössbauer spectroscopy is a useful technique usually utilized for understanding site location of the impurity atoms in a lattice and the formation of defect complexes. The focus of this dissertation is the study of lattice location of ion implanted ⁵⁷Mn/⁵⁷Fe ions in the III-V semiconductors InP, n-type InAs and p type InAs, and the annealing of implantation induced lattice damage in these samples. ⁵⁷Fe Mössbauer spectroscopy studies have been conducted on III-V semiconductors InP, n-type InAs and p-type InAs with the 57Fe Mössbauer state being populated following the implantation of radioactive ⁵⁷Mn⁺ ions which has the advantage that extremely low fluence implantations are sufficient to give data with good statistics. The ⁵⁷Mn⁺ ions were accelerated to 60 keV at the ISOLDE/CERN facility and implanted with fluences of up to 2x10¹² ions/cm² into single crystal samples which were held at 300 –700 K in an implantation chamber. βdecay of the Mn⁺ imparts an average recoil energy of 40 keV to the daughter ⁵⁷*Fe which are then re-distributed onto interstitial and/or substitutional sites, or trapped in defect complexes and damage sites. The Mössbauer spectra were collected with a light-weight parallel plate avalanche counter, with ⁵⁷Fe enriched stainless steel electrodes, mounted on a conventional drive unit outside the implantation chamber. The spectra were analyzed with the Mössbauer fitting code VINDA which allowed for simultaneous fits of the set of spectra for each sample collected at different temperatures. Acceptable fits to the Mössbauer spectra of the InP, n-type InAs and p-type InAs samples required three components: an asymmetric doublet attributed to Fe atoms in implantation induced damaged environments, a single line assigned to Fe on substitutional In sites, and a weak symmetric doublet assigned to impurity-vacancy complexes. In InP there is already an appreciable substitutional Fe (Feѕ) fraction on implantation at room temperature; while in the InAs samples FeS only becomes significant above 400 K. In all samples, the asymmetric doublet dominates the spectra below 400 K. Implantation damage, however, anneals quite rapidly and at high temperatures (above 400 K), the single line due to Feѕ dominates the spectra while the Fe-defect complex dissociates at 500 K. The implantation induced damage is observed to anneal fast in the arsenide samples compared to the phosphide sample. The slow annealing of the damage in InP was supported by the higher Debye temperature (290 K) extracted from the temperature dependence of the site population for the damage site in InP compared with InAs (194 K and 200 K for n-type and p-type, respectively). Variations in the isomer shift and quadrupole splitting for the damage site in InP at high temperatures (above 400 K) suggest structural changes in the neighborhood of the ⁵⁷Fe probe. Furthermore, the isomer shifts of the spectral components were consistent with near trivalent state and fully trivalent state i.e., Fe³⁺ with d⁵ electron configuration for Fe ions in the damage site and at the substitutional (In) site, respectively. The impurity Fe atoms associated with vacancies are identified to be in the Fe²⁺ state with a d⁶ electron configuration. ________________________________________________________________ / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

The behaviour of the crossfield current-driven ion acoustic instability in a plasma containing two ion species is theoretically examined. In our model the electrons are assumed to be hot and the ions cold, i.e. Tₑ »Tᵢ (~ 0), where both ion species are given the same temperature. The length and time scales are such that the electrons are magnetized and the ions unmagnetized. The linearised Vlasov equation is used to set up a dispersion relation for electrostatic waves for Maxwellian equilibrium velocity distributions of the electrons and ions. For the ion acoustic wave, a study is made of the dependence of the critical electron drift velocity (Vͨₒ) required to excite an instability on several parameters. The parameters include light ion fraction, heavy to light ion mass ratio, magnetic field strength and the propagation angle. In general the maximum value of Vͨₒ is found to be smaller than that for an unmagnetized plasma. Approximate analytic solutions of the dispersion relation are used to make comparisons with solutions from the full dispersion relation. The effect of drifts due to inhomogeneities in external magnetic field, perpendicular electron temperature and electron density on the growth rate of the ion acoustic instability are investigated in the ion rest frame. Finally, in a reference frame in which the electrons are stationary, both ion species are given external drifts. The effects of the ion drift velocities (both equal and unequal), electron to ion temperature ratio, light ion fraction, and heavy to light ion mass ratio on the growth rate of the ion acoustic instability are then studied. / Thesis (M.Sc.)-University of Durban-Westville, 1987.

This thesis gives an outline of the ionosphere and studies that were conducted to investigate / Thesis (M.Sc.) - University of KwaZulu-Natal, 2009.