Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: We are studying a possible implementation of an appropriate framework for a proper non- Hermitian quantum theory. We present the case where for a non-Hermitian Hamiltonian with real eigenvalues, we define a new inner product on the Hilbert space with respect to which the non-Hermitian Hamiltonian is Quasi-Hermitian. The Quasi-hermiticity of the Hamiltonian introduces the bi-orthogonality between the left-hand eigenstates and the right-hand eigenstates, in which case the metric becomes a basis transformation. We use the non-Hermitian quadratic Hamiltonian to show that such a metric is not unique but can be uniquely defined by requiring to hermitize all elements of one of the irreducible sets defined on the set of all observables. We compare the constructed metric with specific known examples in the literature in which cases a unique choice is made. / AFRIKAANSE OPSOMMING: Ons ondersoek die implementering van n gepaste raamwerk virn nie-Hermitiese kwantumteorie. Ons beskoun nie-Hermitiese Hamilton-operator met reele eiewaardes en definieer in gepaste binneproduk ten opsigtewaarvan die operator kwasi-Hermitiese is. Die kwasi- Hermities aard van die Hamilton operator lei dan tot n stel bi-ortogonale toestande. Ons konstrueer n basistransformasie wat die linker en regter eietoestande van hierdie stel koppel. Hierdie transformasie word dan gebruik omn nuwe binneproduk op die Hilbert-ruimte te definieer. Die oorspronklike nie-HermitieseHamilton-operator is danHermitiesmet betrekking tot hierdie nuwe binneproduk. Ons gebruik die nie-Hermitiese kwadratieseHamilton-operator omte toon dat hierdie metriek nie uniek is nie, maar wel uniek bepaal kan word deur verder te vereis dat dit al die elemente van n onherleibare versameling operatoreHermitiseer. Ons vergelyk hierdie konstruksiemet die bekende voorbeelde in die literatuur en toon dat diemetriek in beide gevalle uniek bepaal kan word.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Two problems in the field of materials-based condensed matter physics, specifically in the field of superconductivity, are studied theoretically. In both problems, where each is of current exper- imental interest, an extension of Ginzburg-Landau theory is used to describe a physical system, with focus on the energy associated to the interface(s) occurring in the respective systems. The first physical system under consideration is that of a two-band superconductor. Using Ginzburg-Landau theory for two-band superconductors, the interface energy ¾s between normal and superconducting states coexisting at the thermodynamic critical magnetic field is determined. From the theoretical and numerical analysis of the interface energy, it is found that close to the transition temperature, where the Ginzburg-Landau theory is applicable, the two-band problem maps onto an effective single band problem. This finding puts into question the possibility of intermediate, so called type-1.5 superconductivity, in the regime where the Ginzburg-Landau theory applies. The second physical system is that of a system with competing superconductivity and anti- ferromagnetism. From Ginzburg-Landau theory for such competing systems in a thermodynamic critical magnetic field, it is shown that two possible interfaces can occur: an interface between a pure anti-ferromagnetic state and a pure superconducting state; and an interface between a state with coexisting superconductivity and anti-ferromagnetism and a pure anti-ferromagnetic state. The energy associated to both these interfaces is analysed theoretically and numerically from which the boundary between type-I and type-II superconductivity is obtained for certain specific cases. / AFRIKAANSE OPSOMMING: Twee probleme in die veld van materiaal-gebaseerde gekondenseerde materie fisika, spesifiek in die veld van supergeleiding, word teoreties bestudeer. In beide probleme, albei tans van eksper- imentele belang, word ’n fisiese sisteem beskryf deur ’n uitbreiding van enkel-band Ginzburg- Landau teorie, met fokus op die energie geassosieer met die koppelvlak(ke) wat in die onderskeie sisteme aangetref word. Die eerste fisiese sisteem wat beskou word is die van ’n twee-band supergeleier. Deur van Ginzburg-Landau teorie vir twee-band supergeleiers gebruik te maak, word die koppelvlak energie ¾s tussen die gelyktydig bestaande normaal- en supergeleidende toestand in die termodinamiese kritieke magneetveld bepaal. Deur beide teoretiese en numeriese analieses word bepaal dat na aan die oorgangstemperatuur, waar Ginzburg-Landau teorie geldig is, die twee-band probleem op ’n effektiewe een-band probleem afbeeld. Hierdie bevinding bevraagteken dus die moontlikheid van onkonvensionele, of sogenaamde tipe-1.5 supergeleiding, vir gevalle waar Ginzburg-Landau teorie geldig is. Die tweede fisiese siteem wat beskou word is ’n sisteem met kompeterende supergeleiding en anti-ferromagnetisme. Met behulp van Ginzburg-Landau teorie vir sulke sisteme in ’n termod- inamiese kritiese magneetveld word gewys dat daar twee moontlike koppelvlakke kan ontstaan: ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n uitsluitlik supergeleidende toestand; sowel as ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n toes- tand van beide supergeleiding en anti-ferromagnetisme. Die energie geassosieer met beide hierdie koppelvlakke word teoreties en numeries geanaliseer wat lei tot ’n beskrywing van die grenslyn tussen tipe-I en tipe-II supergeleiding in sekere spesifieke gevalle.

Thesis (MSc (Physics))--University of Stellenbosch, 2009. / The exciting field of ultrashort laser optics has experienced tremendous growth since it's inception. One of it's branches that has been of continuous interest is the characterization of ultrashort laser pulses ...

Thesis (MSc (Physics))--Stellenbosch University, 2008. / Third harmonic generation (THG) in a metal vapour is a nonlinear optical interaction that facilitates the generation of light in the vacuum ultraviolet (VUV) portion of the electromagnetic spectrum. The requirement of the metal vapour medium is that it has a suitably large third order nonlinear susceptibility. The third order susceptibility is further enhanced by a two photon resonance. Zinc and magnesium vapours are such nonlinear media. The THG process can be phase matched by mixing the metal vapour with a noble gas in a speci c pressure ratio. The metal vapour noble gas mixture needs to be homogeneous and its temperature needs to be constant to within less than a degree Celsius over a path length of 7 cm. These requirements are satis ed by a crossed heat pipe oven. The heat pipe oven makes use of a dynamic liquid-vapour phase equilibrium in sodium in order to maintain a constant temperature of around 800 degrees Celsius, thus facilitating the generation of a stable homogeneous medium of metal vapour and noble gas that can be used for e cient generation of VUV radiation. The development of such a VUV source using zinc vapour and the application of a similar VUV source using magnesium vapour are discussed. The VUV radiation has been applied to laser induced uorescence spectroscopy of carbon monoxide (12C16O and 13C16O). Spectral lines of 20 spin-forbidden singlet-triplet transitions of the e3 − − X1 +(5 0) band were detected and accurate experimental wavelengths determined for the rst time for ve of these lines.

Thesis (MSc (Physics))--University of Stellenbosch, 2008. / Various autocorrelation techniques are employed to characterize ultrashort laser pulses in both the temporal and spectral domain. These techniques are; interference autocorrelation (IAC), modified spectrum autointerferometric correlation (MOSAIC), background-free autocorrelation (BFA) and frequency resolved optical gating (FROG). All of these techniques are based on the interaction of a pulse with a time delayed copy of itself within a Â(2) medium. Experimental setups for BFA and FROG experiments are developed, which exploit the phenomenon of second harmonic generation (SHG). An existing IAC setup is used for temporal pulse characterization. MOSAIC results are obtained through applying a specific Fourier filter to the IAC data. IAC and MOSAIC measurements performed on a commercially available femtosecond laser, indicate that the emitted pulse has a pulse duration less than 150 fs and possesses positive linear chirp. BFA and FROG measurements carried out on the same laser system mirror these results. Pulses emitted by a 20 Hz chirped pulse amplifier are characterized through BFA and FROG. BFA results suggest that the pulse from the amplifier is actually a double pulse. FROG results indicate that the pulse is highly chirped. The experiments and physical interpretations presented in this work demonstrate the preferred methods of optical pulse characterization for ultrashort laser pulses.

Thesis (MSc (Physics))--University of Stellenbosch, 2005. / The extremely high light intensities produced by lasers and the increasing use of lasers highlights the need for measures to prevent damage to materials due to exposure to high intensity laser light. In particular it necessitates the development of systems to protect optical sensors, including the human eye. In this work optical limiters were investigated as a system for protecting sensors. An optical limiter transmits ambient light, but absorbs high intensity light. This makes it ideal for protecting sensors from laser radiation, since it allows the sensor to operate unhindered at design intensities while protecting it from harmful high intensity radiation. There are various mechanisms used for optical limiting, and in this work the nonlinear absorption and the nonlinear index of refraction changes of materials were investigated. A facility was established to measure the nonlinear optical properties of a variety of materials, in order to classify them as possible optical limiters. This entailed creating a so called Zscan setup, which enabled us to measure the nonlinear absorption coefficient and the nonlinear index of refraction of a material. The theory and the design of the setup are discussed and experimental results obtained using this setup are presented. A wide variety of material types were investigated to show the versatility of the experimental setup. These included C60, which was analyzed in solution; ZnO which is a crystal; CdS quantum dots in solution; and poly(dioctyl-fluorene), which is a large polymer molecule, in solution. The materials investigated in this work were chosen based on their known strong nonlinear optical properties. Emphasis was placed on measuring the nonlinear absorption coefficients since it was the dominant optical limiting effect of the materials under investigation. The results obtained displayed the same trends as published results and it shows that the established facility was capable of measuring the nonlinear properties of these samples. The experimental limitations of the setup were determined, and critical experimental parameters were identified for measurements of this nature. Improvements to the experimental facility are suggested to improve the accuracy of future measurements.

Thesis (MSc)--University of Stellenbosch, 2007. / Please refer to full text for abstract

Thesis (MSc (Physics))--University of Stellenbosch, 2005. / A tunable vacuum ultra-violet (VUV) laser source was recently developed for VUV spectroscopy using state selective excitation and total fluorescence detection. The VUV laser source makes use of a four-wave mixing process to provide tunable VUV radiation for the electronic excitation of the molecules. The theory of four-wave mixing, with the emphasis on parameters that are important for our experimental setup to generate efficient tunable VUV radiation is discussed. The experimental setup, and in particular the metal vapor heat-pipe, which provides Mg vapor as the nonlinear medium, is described. New diagnostic equipment described in this work was added to the experimental setup. This equipment was characterized and utilized together with the existing setup. The additional diagnostic equipment introduced enabled us to measure the tunable VUV output of the source (using a VUV monochromator), making it possible to significantly improve the efficiency of the existing tunable VUV laser source.

Thesis (MSc (Physics))--University of Stellenbosch, 2006. / The aim of this thesis is the semi-classical implementation of Wegner’s flow equations and comparison with the well-established Wentzel-Kramers-Brillouin method. We do this by converting operators, in particular the Hamiltonian, into scalar functions, while an isomorphism with the operator product is maintained by the introduction of the Moyal product. A flow equation in terms of these scalar functions is set up and then approximated by expanding it to first order in ~. We apply this method to two potentials, namely the quartic anharmonic oscillator and the symmetric double-well potential. Results obtained via the flow equations are then compared with those obtained from the WKB method.

Thesis (MSc (Physics))--University of Stellenbosch, 2007. / In this thesis we present a relativistic formalism for the description of hypernuclei production via the weak interaction. It will be shown that the cross section can be written as the contraction of a leptonic and hadronic tensor if we model the interaction as a quasifree process. The hadronic tensor is written in a model-independent way in terms of thirteen nuclear structure functions. A Born term model is used to describe the underlying elementary hyperon production process. The bound state wave functions of the hyperon and nucleon are calculated within a relativistic mean-field approximation. Together with the relativistic kinematics a fully relativistic framework for experimental predictions is constructed and a specific cross section calculation is discussed.