Dynamical tunneling in systems with a mixed phase space [Elektronische Ressource] / vorgelegt von Steffen Löck

Dynamical Tunnelingin Systems with a Mixed Phase SpaceDissertationzur Erlangung des akademischen GradesDoctor rerum naturaliumvorgelegt vonSteffen Löckgeboren am 22.03.1982 in RadebeulInstitut für Theoretische PhysikFachrichtung PhysikFakultät für Mathematik und NaturwissenschaftenTechnische Universität Dresden2009Eingereicht am 16.12.20091. Gutachter: Prof. Dr. Roland Ketzmerick2. Gutachter: Prof. Dr. Jan WiersigVerteidigt am 22.04.2010vAbstractTunneling is one of the most prominent features of quantum mechanics. While the tunnelingprocess in one-dimensional integrable systems is well understood, its quantitative prediction forsystems with a mixed phase space is a long-standing open challenge. In such systems regionsof regular and chaotic dynamics coexist in phase space, which are classically separated butquantum mechanically coupled by the process of dynamical tunneling. We derive a predictionof dynamical tunneling rates which describe the decay of states localized inside the regularregion towards the so-called chaotic sea. This approach uses a fictitious integrable systemwhich mimics the dynamics inside the regular domain and extends it into the chaotic region.Excellent agreement with numerical data is found for kicked systems, billiards, and opticalmicrocavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinearresonance chains dominate the tunneling process.