Quantum ergodicity and localization in conservative systems: The Wigner band random matrix model

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, are presented for the Wigner band random matrix ensemble, which is believed to provide a description for a broad class of conservative quantum systems which are strongly chaotic in the classical limit. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.