Herman-Kluk semiclassical dynamics in action-angle representation: new approaches to mapping quantum degrees of freedom.

A general approach to mapping a discrete quantum mechanical problem by a continuous Hamiltonian is presented. The method is based on the representation of the quantum number by a continuous action variable that extends from -infinity to infinity. The projection of this Hilbert space onto the set of integer quantum numbers reduces the Hamiltonian to a discrete matrix of interest. The theory allows the application of the semiclassical methods to discrete quantum mechanical problems and, in particular, to problems where quantum Hamiltonians are coupled to continuous degrees of freedom. The Herman Kluk semiclassical propagation is used to calculate the nonadiabatic dynamics for a model avoided crossing system. The results demonstrate several advantages of the new theory compared to the existing mapping approaches.