Semiclassical approximations for single eigenstates of quantum maps [Elektronische Ressource] / vorgelegt von Martin Sczyrba

Max-Planck-Institut fur Physik komplexer SystemeSemiclassical approximations for singleeigenstates of quantum mapsder Fakult at fur Mathematik und Naturwissenschaftender Technischen Universit at Dresden vorgelegteDissertationzur Erlangung des akademischen Grades der NaturwissenschaftenDoctor rerum naturalium(Dr.rer.nat.)vorgelegt vonMartin SczyrbaDresden 20031. Gutachter: Prof. Dr. J.-M. Rost2. Gutachter: Prof. Dr. R. Ketzmerick3. Gutachter: Prof. Dr. K. RichterDatum des Einreichens der Arbeit: 08.01.2003AbstractThis dissertation discusses the possibilities and the limitations of Fredholm’s method for thesemiclassical study of single eigenstates of quantum maps.The Fredholm method provides a scheme that allows the systematic evaluation of eigenstates.It was previously applied to eigenstates which correspond to non-degenerate eigenvalues. Thus,it can not be used for the evaluation of many eigenstates of common systems, for examplequantum cat maps. Therefore, within the framework of Fredholm’s method the full eigenvalueproblem will be solved. This means that eigenstates corresponding to degenerate eigenvaluescan also be evaluated. In the form derived in this work, Fredholm’s method can be applied toall eigenstates of a quantum map. It provides a representation of single eigenstates in termsof powers of the propagator of the quantum map. By using this representation parametriccorrelations of single eigenstates can also be semiclassically calculated.