  The correlation between overlap intensities and level velocities has been
introduced as a sensitive measure capable of revealing phase space
localization. Previously applied to chaotic quantum systems, here we extend the
theory to near-integrable and mixed quantum systems. This measure is useful in
the latter cases because it has the ability to highlight certain phase space
structures depending upon the perturbation used to parametrically vary the
Hamiltonian. A detailed semiclassical theory is presented relating the
correlation coefficient to the phase space weighted derivatives of the
classical action. In the process, we confront the question of whether the
Hannay-Ozorio de Almeida sum rules are simply extendable to mixed phase space
systems. In addition, the hbar-scalings of the correlation coefficient and
relevant quantities are derived for nearly integrable systems. Excellent
agreement is found between the theory and the results for integrable billiards
as well as for the standard map.
