Survival probability and local density of states for one-dimensional Hamiltonian systems

For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between 'perturbative' and 'non-perturbative' regimes, and to the observation that semiclassical tools are useful in the latter case. We discuss what is 'left' from this theory in the case of one-dimensional systems. We demonstrate that the remarkably accurate uniform semiclassical approximation captures the physics of all the different regimes, though it cannot take into account the effect of strong localization.