Thesis (MSc)--Stellenbosch University, 2003. / ENGLISH 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. / AFRIKAANSE 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/53428 |
| Date | 03 1900 |
| Creators | Bartlett, Bruce |
| Contributors | Scholtz, F. G., Geyer, H. B., Stellenbosch University. Faculty of Science. Dept. of Physics . |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 78 p. : ill. |
| Rights | Stellenbosch University |
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