Role that separatrices and stochastic webs play in quantum dynamics

We numerically analyze the influence of separatrices and stochastic webs on the evolution of quantum wave functions in phase space and we compare our findings with the corresponding classical evolution. We study the dynamics in regular and nonregular systems, namely, in a quartic, the pendulum, and the kicked harmonic oscillator potentials. Regardless of the specific potential, there are common features in the dynamics, some of which are revealed when very small parts of the quantum phase-space densities are analyzed.