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Non-perturbative flow equations from continuous unitary transformations
Thesis (MSc (Physics))--University of Stellenbosch, 2005.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867613940439056384 |
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| access_status_str | Open Access |
| author | Kriel, Johannes Nicolaas |
| author2 | Scholtz, Frederik G. |
| author_browse | Kriel, Johannes Nicolaas Scholtz, Frederik G. |
| author_facet | Scholtz, Frederik G. Kriel, Johannes Nicolaas |
| author_sort | Kriel, Johannes Nicolaas |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Physics))--University of Stellenbosch, 2005. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/3125 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:07.837Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/3125 Non-perturbative flow equations from continuous unitary transformations Kriel, Johannes Nicolaas Scholtz, Frederik G. Geyer, H. B. University of Stellenbosch. Faculty of Science. Dept. of Physics. Dissertations -- Physics Theses -- Physics Unitary transformations Flow equations Thesis (MSc (Physics))--University of Stellenbosch, 2005. The goal of this thesis is the development and implementation of a non-perturbative solution method for Wegner’s flow equations. We show that a parameterization of the flowing Hamiltonian in terms of a scalar function allows the flow equation to be rewritten as a nonlinear partial differential equation. The implementation is non-perturbative in that the derivation of the PDE is based on an expansion controlled by the size of the system rather than the coupling constant. We apply this method to the Lipkin model and obtain very accurate results for the spectrum, expectation values and eigenstates for all values of the coupling and in the thermodynamic limit. New aspects of the phase structure, made apparent by this non-perturbative treatment, are also investigated. The Dicke model is treated using a two-step diagonalization procedure which illustrates how an effective Hamiltonian may be constructed and subsequently solved within this framework. 2008-07-16T09:21:11Z 2010-06-01T09:06:57Z 2008-07-16T09:21:11Z 2010-06-01T09:06:57Z 2005-12 Thesis http://hdl.handle.net/10019.1/3125 en University of Stellenbosch application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Dissertations -- Physics Theses -- Physics Unitary transformations Flow equations Kriel, Johannes Nicolaas Non-perturbative flow equations from continuous unitary transformations |
| title | Non-perturbative flow equations from continuous unitary transformations |
| title_full | Non-perturbative flow equations from continuous unitary transformations |
| title_fullStr | Non-perturbative flow equations from continuous unitary transformations |
| title_full_unstemmed | Non-perturbative flow equations from continuous unitary transformations |
| title_short | Non-perturbative flow equations from continuous unitary transformations |
| title_sort | non perturbative flow equations from continuous unitary transformations |
| topic | Dissertations -- Physics Theses -- Physics Unitary transformations Flow equations |
| url | http://hdl.handle.net/10019.1/3125 |
| work_keys_str_mv | AT krieljohannesnicolaas nonperturbativeflowequationsfromcontinuousunitarytransformations |