Stability of quantum motion in chaotic and regular systems

The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.