Parametric Variation of Chaotic Eigenstates and Phase Space Localization

We investigate the phase space localization properties of eigenstates of a quantum system possessing a chaotic classical limit. Parametric variation of the system suggests introducing a measure of correlations between state overlap intensities and level velocities to infer information about the extent of eigenstate localization. Random matrix theory predicts no correlations. Yet when applied to the chaotic stadium billiard, we find large correlations reflecting the significant eigenstate scarring due to the parametric action variations of the orbits homoclinic to the central trajectory underlying the wave packet. The analysis can be applied to data taken with quantum dots in the Coulomb-blockade regime and microwave cavities.