Stability of wave packet dynamics under perturbations
  We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. 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 realised for inverted harmonic oscillators. 
Jens Bolte and Tobias Schwaibold