Dynamical Tunneling and its Application to Spectral Statistics

Tunneling is a central result of quantum mechanics. It allows quantum particles to enter regions which are inaccessible by classical dynamics. Consequences of the tunneling process are most relevant. For example it causes the alpha-decay of radioactive nuclei and it is argued that proton tunneling is decisive for the emergence of DNA mutations. The theoretical prediction of corresponding tunneling rates is explained in standard textbooks on quantum mechanics for regular systems. Typical physical systems such as atoms or molecules, however, also show chaotic motion. Here the calculation of tunneling rates is more demanding. In this text a selection of articles on the prediction of tunneling rates in systems which allow for regular and chaotic motion is summarized. The presented approach is then used to explain consequences of tunneling on the quantum spectrum, such as the universal power-law behavior of small energy spacings and the flooding of regular states