Fractional revivals in systems with two time scales

We examine the dynamical evolution of wave packets in a large class of quantum systems where two quantum numbers determine the energy spectrum and consequently the dynamical behavior. Using a generic Hamiltonian, we study the formation of coherent structures. The ratio of two time scales as well as the symmetry of the initial wave packet decisively determines the revival and fractional revivals of the system for which we give analytical results. The theory is applicable to a wide class of systems from diatomic molecules to ions in two-dimensional traps and two interacting Bose condensates.