Representation Theoretical Construction of the Classical Limit and Spectral Statistics of Generic Hamiltonian Operators

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dc.creatorSchäfer, Ingolf
dc.date2006-12-27
dc.date.accessioned2026-07-07T07:37:16Z
dc.date.available2026-07-07T07:37:16Z
dc.descriptionStarting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction in chapter 1 this problem is motivated by a general construction of the classical limit for quantum mechanical systems, which is adopted to this setting, in chapter 2. In chapter 3 it is shown that for simple operators, i.e., operators of the Lie algebra the nearest neighbor statistics along a sequence of irreducible representations converge to the Dirac measure. After a suitable completion of the universal enveloping algebra the convergence to Poisson statistics is proved in chapter 4 for the exponentials of generic operators. The proof makes use of a combinatorial inequality of the Katz-Sarnak type for tori, which is proved in chapter 5. In the appendix the necessary facts from group theory and the theory of nearest neighbor distributions are gathered.
dc.description80 pages, 5 figures, phd thesis of the author
dc.identifierhttps://arxiv.org/abs/math/0612780
dc.identifierhttp://arxiv.org/abs/math/0612780
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120717
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subject22E46
dc.titleRepresentation Theoretical Construction of the Classical Limit and Spectral Statistics of Generic Hamiltonian Operators
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