Recurrence statistics of observables in quantum-mechanical wave packet dynamics

We investigate the recurrence properties of the time series of quantum-mechanical expectation values, in terms of representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence time distributions, return maps and recurrence plots, we show that when the nonlinearity is sufficiently high, the expectation values of appropriate observables pertaining to the field can exhibit features characteristic of hyperbolic classical dynamical systems, even though the total Hamiltonian has a discrete spectrum