# Flow equations for hamiltonians from continuous unitary transformations

Bartlett, Bruce (2003-03)

Thesis (MSc)--Stellenbosch University, 2003.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/53428

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