Flow equations for hamiltonians from continuous unitary transformations

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dc.contributor.advisorScholtz, Frederik G.en_ZA
dc.contributor.advisorGeyer, H. B.
dc.contributor.authorBartlett, Bruce
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Physics .en_ZA
dc.date.accessioned2012-08-27T11:35:28Z
dc.date.available2012-08-27T11:35:28Z
dc.date.issued2003-03
dc.descriptionThesis (MSc)--Stellenbosch University, 2003.
dc.description.abstractENGLISH ABSTRACT: This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework is established in the initial chapter and used as a background for the entire presentation. The application of flow equations to the Foldy-Wouthuysen transformation and to the elimination of the electron-phonon coupling in a solid is reviewed. Recent flow equations approaches to the Lipkin model are examined thoroughly, paying special attention to their utility near the phase change boundary. We present more robust schemes by requiring that expectation values be flow dependent; either through a variational or self-consistent calculation. The similarity renormalization group equations recently developed by Glazek and Wilson are also reviewed. Their relationship to Wegner's flow equations is investigated through the aid of an instructive model.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Hierdie tesis bied 'n oorsig van die vloeivergelykings soos dit onlangs deur Wegner voorgestel is. Die betreklik onbekende wiskundige raamwerk word in die eerste hoofstuk geskets en deurgans as agtergrond gebruik. 'n Oorsig word gegee van die aanwending van die vloeivergelyking vir die Foldy-Wouthuysen transformasie en die eliminering van die elektron-fonon wisselwerking in 'n vastestof. Onlangse benaderings tot die Lipkin model, deur middel van vloeivergelykings, word ook deeglik ondersoek. Besondere aandag word gegee aan hul aanwending naby fasegrense. 'n Meer stewige skema word voorgestel deur te vereis dat verwagtingswaardes vloei-afhanklik is; óf deur gevarieerde óf self-konsistente berekenings. 'n Inleiding tot die gelyksoortigheids renormerings groep vergelykings, soos onlangs ontwikkel deur Glazek en Wilson, word ook aangebied. Hulle verwantskap met die Wegner vloeivergelykings word bespreek aan die hand van 'n instruktiewe voorbeeld.af_ZA
dc.format.extent78 p. : ill.
dc.identifier.urihttp://hdl.handle.net/10019.1/53428
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectHamiltonian systemsen_ZA
dc.subjectEquationsen_ZA
dc.subjectUnitary transformationsen_ZA
dc.subjectDissertations -- Physicsen_ZA
dc.subjectTheses -- Physicsen_ZA
dc.titleFlow equations for hamiltonians from continuous unitary transformationsen_ZA
dc.typeThesisen_ZA
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