Oeljeklaus, EberhardSchäfer, IngolfIngolfSchäfer2020-03-092020-03-092006-11-09https://media.suub.uni-bremen.de/handle/elib/2291Starting 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., operator 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.enBitte wählen Sie eine Lizenz aus: (Unsere Empfehlung: CC-BY)Classical LimitRepresentation TheoryRandom Matrix Theory510Dissertationurn:nbn:de:gbv:46-diss000104949