A spectroscopical measure for the exploration of phase space

Many nonintegrable systems have eigenstates that typically require numerous basis states to represent them. We develop a criterion to judge the extent to which phase space is explored by the spectrum of such a Hamiltonian. Our criterion uses the eigenvalues rather than the eigenfunctions and is based on identifying a direct relation between the intensity of Shnirelman's peak and the localization length. We illustrate our procedure by applying it to the spectrum of two prototypical nonintegrable systems, the kicked rotor and the kicked top. (c) 1998 American Institute of Physics.