Exploring phase space localization of chaotic eigenstates via parametric variation - art. no. 016208

In a previous paper [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation m easure was introduced that sensitively probes phase space localization prop erties of eigenstates. It is based on a system's response to varying an ext ernal parameter. The measure correlates level velocities with overlap inten sities 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 (h) over bar dependence, and demonstrate the agreement between this measure and a semic lassical theory based on homoclinic orbits.