Scaling of the average survival probability for low dimensional systems

Recent conjectures put forward by Schofield and Wolynes regarding the scaling behaviour of averaged survival probabilities are tested in an extreme limit. The system of choice is the quasi 3-dimensional Baggotʹs spectroscopic Hamiltonian for H2O. Despite the low density of states for the system, the survival probability when averaged over the states of a given polyad shows the expected scaling with the resonance coupling. Power law behaviour, for intermediate times, is observed for both classically integrable and non-integrable systems. The power law behaviour persists even when the accompanying fluctuations, possibly due to quantum twinkling in the system, are very large. However, among the integrable subsystems of the full Hamiltonian the 1:1 resonance case exhibits an anomalously large exponent.