Stability of quantum motion: Beyond Fermi-golden-rule and Lyapunov decay

The stability of quantum motion for a classically chaotic system is discussed. The existence of different regimes of fidelity decay is shown. The deviations from Fermi-golden-rule and Lyapunov regimes are observed when the underlying classical dynamics is weakly chaotic. It is found that fidelity is an important quantity which characterizes the stability of quantum and classical systems.