Phase space localization of chaotic eigenstates: Violating ergodicity - art. no. 016209

The correlation between level velocities and eigenfunction intensities prov ides a new way of exploring phase space localization in quantized nonintegr able systems. It can also serve as a measure of deviations from ergodicity due to quantum effects for typical observables. This paper relies on two we ll known paradigms of quantum chaos, the bakers map and the standard map, t o study correlations in simple, yet chaotic, dynamical systems. The behavio rs are dominated by the presence of several classical structures. These pri marily include short periodic orbits and their homoclinic excursions. The d ependences of the correlations deriving from perturbations allow for eigenf unction features violating ergodicity to be selectively highlighted. A semi classical theory based on periodic orbit sums leads to certain classical co rrelations that are superexponentially cut off beyond a logarithmic time sc ale. The theory is seen to be quite successful in reproducing many of the q uantum localization features.