Systems modelling nanoscale structures have been studied in the context of the theory of energy level statistics in the ballistic and mesoscopic as well as the insulating regimes. Statistics were obtained using a new unfolding scheme based on the existence of a local stationary property for fluctuations of the energy spectra. Two different models were used in the study with particular emphasis on the relevance to the physics of nanoscale devices. Thus, a quantum billiard model composed of a quasi-two-dimensional tight-binding atomic lattice was introduced. The results of the statistical analysis of the spectra of the models were compared throughout the thesis with Random Matrix Theory (RMT). The applicability of RMT and the universality predicted by RMT were verified. / The statistical behavior of energy levels for systems in the crossover region between regular and chaotic behavior was studied in all three regimes. Gradual transitions were observed for both ballistic and mesoscopic systems, and found to be similar in the cases. For systems in the insulating regime, the statistical behavior of levels was found to be of Poisson type. The transition from GOE to Poisson behavior when the system is changed from the mesoscopic to the insulating regime was also studied, a spectral dependence of the local fluctuations of energy levels was found, indicating the break-down of translation invariance of the local fluctuations. / The transition due to time reversal invariant symmetry breaking was studied by applying a uniform magnetic field to systems constructed by using a tight-binding model with non-zero off-diagonal interactions. By rescaling the transition control parameter, it was found that for both ballistic and mesoscopic systems the transition behavior can be well described by RMT. For closed systems the transition is complete when the effective area of the system encloses a flux greater than one flux quantum.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.40022 |
| Date | January 1995 |
| Creators | Yan, Zhi Da |
| Contributors | Harris, Richard (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001487275, proquestno: NN12514, Theses scanned by UMI/ProQuest. |
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