Thesis (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: In this thesis, generalized Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalized Dyson boson-fermion mapping, or a Dyson mapping for short, is a one-to-one linear but non-unitary operator that can be applied to vectors representing the states of a many-fermion system. A vector representing a fermion system maps onto a vector that is most naturally interpreted as representing a state of a many-body system that contains both bosons and fermions. The motivation for doing such a mapping is the hope that the mapping will reveal some property of the system that simplifies its analysis and that was hidden in the original form. The aims of this thesis are 1. to review the theory of generalized Dyson boson-fermion mappings, 2. by considering a tutorial example, to demonstrate that it is feasible to implement the theory and 3. to find a useful application for a generalized Dyson boson-fermion mapping, by considering a non-trivial model, namely the Richardson model for superconductivity. The realization of the first two aims mainly involve the collecting together of ideas that have already appeared in the literature, into one coherent text. Some subtle points that were treated only briefly due to space restrictions in the journal publications where the theory was first expounded, are elaborated on in the present work. On the other hand, the analysis of the Richardson Hamiltonian that uses a Dyson mapping, goes beyond what has already appeared in the literature. It is the first time that a boson expansion technique is implemented for a system where the roles of both collective and non-collective fermion pairs are important. (The Dyson mapping associates bosons with Cooper pairs, while the fermions not bound in Cooper pairs result in fermions being present in the mapped system as well.) What is found is that the Dyson mapping uncovers non-trivial properties of the system. These properties aid the construction of time-independent perturbation expansions for the stationary states of the system, as well as time-dependent expansions for transition amplitudes between states. The time-independent expansions agree with results that other authors obtained through methods other than boson expansions. The time-dependent expansions, that one would be hard-pressed to develop without a Dyson mapping, might in future prove useful in understanding aspects of the dynamics of ultracold fermi gases, when time-dependent magnetic fields are used to vary the atom-atom interaction strenght. / AFRIKAANSE OPSOMMING: In hierdie tesis word veralgemeende Dyson boson-fermion-afbeeldings ondersoek. Hierdie afbeeldings word gebruik in die analise van die kwantum veeldeeltjie probleem, en is voorbeelde van sogenaamde boson-uitbreidingstegnieke. 'n Veralgemeende Dyson bosonfermion- afbeelding, of kortweg 'n Dyson afbeelding, is 'n een-tot-een, lineêre maar nie-unitêre operator wat inwerk op vektore wat toestande verteenwoordig van 'n veel-fermion sisteem. 'n Vektor wat 'n fermionsisteem verteenwoordig word so afgebeeld op 'n vektor waarvoor die mees natuurlike interpretasie is dat dit 'n toestand verteenwoordig van 'n sisteem waarin beide bosone en fermione aanwesig is. So 'n afbeelding word gewoonlik gemaak in die hoop dat eienskappe van die sisteem, wat versteek was in die oorspronklike weergawe, voor-die-hand-liggend is na die afbeelding. Hierdie tesis het ten doel 1. om die teorie van veralgemeende Dyson boson-fermion-afbeeldings te hersien, 2. om 'n eenvoudige voorbeeld deur te werk, en so te demonstreer dat die teorie sonder moeite geïmplimenteer kan word en 3. om 'n nuttige toepassing te vind vir 'n veralgemeende Dyson boson-fermion-afbeelding deur 'n nie-triviale model, naamlik die Richardson model vir supergeleiding, te ondersoek. Die eerste twee van hierdie doelwitte behels hoofsaaklik dat idees wat reeds in die literatuur verskyn het, saamgevat word in een koherente teks. Sommige subtiele punte wat, vanwee beperkte ruimte, slegs kortliks bespreek is in die joernaalartikels waarin die teorie oorspronklik verskyn het, word in hierdie tesis meer breedvoering bespreek. Daarteenoor verteenwoordig die analise van die Richardson model met behulp van 'n Dyson afbeelding 'n nuwe bydra. Dit is naamlik die eerste keer dat 'n bosonuitbreiding ingespan word vir 'n sisteem waar sowel kollektiewe as nie-kollektiewe fermionpare 'n belangrike rol speel. (Die Dyson afbeelding assosieer bosone met die oorspronklike sisteem se Cooper pare, terwyl die fermione wat in die oorspronklike sisteem nie tot Cooper pare gebind is nie, sorg dat daar ook fermione teenwoordig is in die afgebeelde sisteem.) Ons vind dat die Dyson afbeelding nie-triviale eienskappe van die sisteem aan die lig bring. Hierdie eienskappe is nuttig vir die konstruksie van beide tyd-onafhanklike steuringsreekse vir die stasionêre toestande van die sisteem en vir tyd-afhanklike steuringsreekse vir oorgangsamplitudes tussen toestande. Die tyd-onafhanklike uitbreidings stem ooreen met resultate wat ander outeurs afgelei het sonder die gebruik van 'n Dyson afbeelding. Die tyd-afhanklike uitbreidings, wat kwalik afgelei kan word sonder 'n Dyson afbeelding, mag vorentoe nuttig wees om aspekte van die dinamika van baie koue Fermi gasse te verstaan, wanneer tydafhanklike magneetvelde gebruik word om die inter-atoomwisselwerking te manipuleer.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 115-118). Also available via the Internet.

Thesis (M.SC.) - Carleton University, 2007. / Includes bibliographical references (p. 103-107). Also available in electronic format on the Internet.

Bhabha scattering, the process of e⁺e⁻ → e⁺e⁻, has been studied at center-of-mass energies from 50 to 58 GeV with the AMY detector at the KEK e⁺e⁻ storage ring TRISTAN. The study is based on a data sample of 79.7 <i>pb⁻¹</i> integrated luminosity. The differential cross section of Bhabha scattering has been measured. The measured cross section is found to agree fairly well with the Standard Model of the electroweak theory. The measured cross section is also compared with various four-fermion contact interaction models, and confidence level lower limits on the composite scale, A, are determined. In addition, the limits on VV model are converted to SM-break-down scales, which indicate the validity of the SM down to the distance of order ~ 10⁻¹⁷ cm and the electron charge radius of ~ 10⁻¹⁶ cm. Attempts are made in searching for an additional boson Z'. No clear signal of the existence of a Z' boson is found up to energy of ~160 GeV/c². The effect of transverse beam polarization on Bhabha scattering is also studied. The ϕ dependence of Bhabha events are fitted to the QED prediction and found to agree with the theory. However, no quantitative conclusion on polarization effect can be drawn based on current data sample, which does not provide enough statistics. More data is being accumulated and further study should be carried out. / Ph. D.

The electron energy loss spectrometer at Virginia Tech has been modified with new momentum deflectors and various other hardware improvements. In addition to some hardware changes all the software to run the spectrometer and analyze the data has been rewritten. It was suggested by Tsuei (1990) that a nested Fermi surface could be used to explain both the fact that these materials have high superconducting transition temperatures and have linear relaxation rates. It was suggested in that same paper that EELS might be able to confirm the presence of Fermi surface nesting. We have attempted to use transmission electron energy loss spectroscopy in a novel way to search for evidence of Fermi surface nesting in the high T_c superconductor Bi₂Sr₂Ca₁Cu₂O₈. High quality single crystal samples were obtained and thinned for use in the EELS. Data was taken at low energy (<1.0eV) and momentum was scanned along three different momentum transfer directions for |q| =0.0 to 3.0Å⁻¹. The data was scaled to be Im(-1/ε). A calculation of Im(-1/ε) was performed using a tight binding model and it was found that the features associated with the Fermi surface (from this TB calculation) were too small to be seen in our spectra. We interpret this problem to be associated with the presence of thermal diffuse scattering. / Ph. D.