Flooding of regular phase space islands by chaotic states [Elektronische Ressource] / vorgelegt von Lars Bittrich

Flooding of Regular Phase Space Islandsby Chaotic StatesDissertationzur Erlangung des akademischen GradesDoctor rerum naturaliumvorgelegt vonLars Bittrichgeboren am 29.06.1981 in GörlitzInstitut für Theoretische PhysikFachrichtung PhysikFakultät für Mathematik und NaturwissenschaftenTechnische Universität Dresden2010Eingereicht am 23. Juni 20101. Gutachter: Prof. Dr. Roland Ketzmerick2. Gutachter: Prof. Dr. Hans-Jürgen StöckmannVerteidigt am 26. Oktober 2010vAbstractWe investigate systems with a mixed phase space, where regular and chaotic dynamics coexist.Classically, regions with regular motion, the regular islands, are dynamically not connected toregions with chaotic motion, the chaotic sea. Typically, this is also reected in the quantumproperties, where eigenstates either concentrate on the regular or the chaotic regions. However,it was shown that quantum mechanically, due to the tunneling process, a coupling is inducedand ooding of regular islands may occur. This happens when the Heisenberg time, the timeneededtoresolvethediscretespectrum, islargerthanthetunnelingtimefromtheregularregionto the chaotic sea. In this case the regular eigenstates disappear. We study this eect by thetimeevolutionofwave packets initially startedinthechaoticseaandndincreasing probabilityintheregularisland. Usingrandommatrixmodelsaquantitative predictionisderived. Wendexcellent agreement with numerical dataobtained forquantum maps andbilliards systems.