Intruder states and their local effect on spectral statistics

The effect on spectral statistics and on the revival probability of intruder states in a random background is analysed numerically and with perturbative methods. For random coupling the intruder does not affect the GOE spectral statistics of the background significantly, while a constant coupling causes very strong correlations at short range with a fourth power dependence of the spectral two-point function at the origin. The revival probability is significantly depressed for constant coupling as compared with random coupling.