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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/3125 |
| Date | 12 1900 |
| Creators | Kriel, Johannes Nicolaas |
| Contributors | Scholtz, F. G., Geyer, H. B., University of Stellenbosch. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Stellenbosch |
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