Scattering signatures of systems with a mixed phase space

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Hamiltonian systems typically show a mixed phase space, i.e. both regular and chaotic dynamics. These properties of the classical dynamics have to be reflected in the more fundamental quantum mechanical description. In addition to the rather well understood quantum properties of completely regular and fully chaotic systems, novel phenomena arise from the coexistence of regular and chaotic dynamics. A lot of progress and surprising results have been obtained for closed systems. It is the central aim of this research project to investigate scattering systems with a mixed phase space. In particular we want to obtain a quantitative understanding of dynamical tunneling rates, describing the transition from a regular island to the chaotic phase-space component, using semi-classical methods. For systems with more than two degrees of freedom with a mixed phase space we want to investigate the structure of eigenstates and scattering signatures of Arnold diffusion.