  In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation
measure was introduced that sensitively probes phase space localization
properties of eigenstates. It is based on a system's response to varying an
external parameter. The measure correlates level velocities with overlap
intensities between the eigenstates and some localized state of interest.
Random matrix theory predicts the absence of such correlations in chaotic
systems whereas in the stadium billiard, a paradigm of chaos, strong
correlations were observed. Here, we develop further the theoretical basis of
that work, extend the stadium results to the full phase space, study the
hbar-dependence, and demonstrate the agreement between this measure and a
semiclassical theory based on homoclinic orbits.
