The non-interacting, nonuniform electron gas exhibits simplifications in two dimensions, that are of particular interest in the application of density functional theory. The results of linear response theory for an attractive impurity in a two-dimensional gas have been shown to be surprisingly accurate even though there are bound states, and were shown to be exact in the high density limit (Zaremba et al. Phys. Rev. B, 71:125323, 2005 and Zaremba et al. Phys. Rev. Lett., 90(4):046801, 2003). The density resulting from linear response theory and the Thomas-Fermi approximation coincide in the high density limit.
As an alternative to linear response theory, the Kirzhnits gradient expansion gives corrections to Thomas-Fermi in gradients of the potential. In two dimensions, all of the gradient corrections vanish at zero temperature, which is a new result presented in this work. We have performed numerical calculations which show that while Thomas-Fermi appears to be a surprisingly accurate approximation in two dimensions, it is not exact. The differences between two and three dimensions that lead to the vanishing of the gradient corrections, however, are of great interest since these may lead to better understanding and simplifications of the corresponding three-dimensional problem. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2007-11-07 09:47:00.316
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/905 |
| Date | 08 November 2007 |
| Creators | Koivisto, Michael William |
| Contributors | Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | 997195 bytes, application/pdf |
| Rights | This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. |
| Relation | Canadian theses |
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