Stability of quantum motion: A semiclassical approach

A semiclassical theory is used for the study of fidelity. For systems with weak chaos in the classical limit, we show that the fidelity has a non-Fermi-Golden-Rule decay, which can be explained by the closeness of the distribution of action difference in the semiclassical theory to the Levy distribution. For systems with strong chaos in the classical limit, we present a semiclassical expression for fidelity decay in the Lyapunov regime, which is more general than the previously predicted Lyapunov decay and lambda(1) decay of fidelity. For systems with regular motion in the classical limit, we derive the fidelity decay for initial narrow Gaussian wavepackets, which displays a quite complex behaviour, from Gaussian to power law decay t(-alpha) with 1 <= a <= 2.