Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states

The idea of perturbation independent decay (PID) has appeared in the context of survival-probability studies, and lately has emerged in the context of quantum irreversibility studies. In both cases the PID reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime. The theory of the survival probability is manifestly related to the parametric theory of the local density of states (LDOS). In this Paper we demonstrate that in spite of the common "ideology", the physics of quantum irreversibility is {\em not} trivially related to the parametric theory of the LDOS. Rather, it is essential to take into account subtle cross correlations which are not captured by the LDOS alone.