The Lame polynomials naturally arise when separating variables in Laplace's equation in elliptic-spherical coordinates. The products of these polynomials form a class of spherical harmonics, which are the joint eigenfunctions of a quantum completely integrable system of commuting, second-order differential operators P0 = DSN , P2,..., PN -1 acting on Cinfinity( SN ). These operators depend on parameters and thus constitute an ensemble. / In the main result presented in this thesis, we compute the limiting mean level spacings distribution for the zeroes of Lame polynomials in various thermodynamic, asymptotic regimes. We give results both in the mean and pointwise, for an asymptotically full set of values of the parameters. As an application, we compute the limiting level spacings distribution of the zeroes of Van Vleck polynomials.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.37872 |
| Date | January 2001 |
| Creators | Bourget, Alain. |
| Contributors | Toth, John A. (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 Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001847775, proquestno: NQ75610, Theses scanned by UMI/ProQuest. |
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