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

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00010494.pdf | 936.09 kB | Adobe PDF | View/Open |

Other Titles: | Darstellungstheoretische Konstruktion des klassischen Grenzfalls und Spektralstatistik generischer Hamiltonoperatoren |

Authors: | Schäfer, Ingolf |

Supervisor: | Oeljeklaus, Eberhard |

1. Expert: | Oeljeklaus, Eberhard |

2. Expert: | Huckleberry, Alan |

Abstract: | Starting 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. |

Keywords: | Classical Limit, Representation Theory, Random Matrix Theory |

Issue Date: | 9-Nov-2006 |

URN: | urn:nbn:de:gbv:46-diss000104949 |

Institution: | Universität Bremen |

Faculty: | FB3 Mathematik/Informatik |

Appears in Collections: | Dissertationen |

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