Stability of wave packet dynamics under perturbations

Details Stability of wave packet dynamics under perturbations Stability of wave packet dynamics under perturbations

2005-09-06

arxiv.org/abs/nlin/0509016v1

Phys. Rev. E 73 (2006) 026223

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.73.026223

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.

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