Bolte, Jens and Schwaibold, Tobias (2006) Stability of wave-packet dynamics under perturbations. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 73 (2).
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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.
This is a Submitted version This version's date is: 2006 This item is not peer reviewed
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