Stability of wave-packet dynamics under perturbations

Abstract

We introduce a method to investigate the stability of wave-packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is nonperturbative. Two separate contributions to the quantum fidelity are identified: one factor derives from the dispersion of the wave packets, whereas the other factor is determined by the separation of a trajectory of the perturbed classical system away from a corresponding unperturbed trajectory. We furthermore estimate both contributions in terms of classical Lyapunov exponents and find a decay of fidelity that is, generically, at least exponential, but may also be doubly exponential. The latter case is shown to be realized for inverted harmonic oscillators.