Time evolution of wave packets in quantum chaotic systems. A manifestation of quantum chaos

The propagation of coherent states in quantum systems is investigated. It is demonstrated both theoretically and numerically that the spatial-temporal evolution of coherent states corresponding to a definite dynamical symmetry under the action of a system with the dynamical symmetry breaking to different extents is corresponding to the motion of a bundle of classical phase trajectories under the same condition. In the condition that the classically chaotic and regular behavior coexist, the propagating characteristics of the coherent states which initially reside in the classically regular region are different from those initially reside in the classically chaotic region indicating that the quantum Hilbert space has the same topological structure of the corresponding classical phase space