Scattering signatures of systems with a mixed phase space

哈密顿系统通常表现为混合相空间，即既有规则动力学又有混沌动力学。经典动力学的这些性质必须反映在更基本的量子力学描述中。除了人们熟知的完全规则和完全混沌系统的量子性质外，规则和混沌动力学的共存还产生了一些新的现象。对于封闭系统，已经取得了许多进展和令人惊讶的结果。研究具有混合相空间的散射系统是本研究项目的中心目标。特别是，我们想要对动态隧穿速率有一个定量的理解，用半经典方法描述从规则孤岛到混沌相空间分量的转变。对于具有两个以上自由度的混合相空间系统，我们要研究Arnold扩散的本征态结构和散射特征。

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.