Semiclassical calculation and analysis of dynamical systems with mixed phase space

A semiclassical method for the propagation of arbitrary wave packets in a multidimensional Hamiltonian is presented. The method is shown to be valid for treating Hamiltonian systems whose classical phase space is a combination of chaotic and quasiperiodic motion (mixed dynamics). The propagation can be carried out long enough for the nonlinearities of the system to be important. The nonlinear dynamics is reflected in spectra and correlation functions. We suggest this new semiclassical method can be a tool for analyzing the nonlinear aspects of the vibrational spectra.