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 matri x ensemble, which is believed to provide a description for a broad cla ss of conservative quantum systems which are strongly chaotic in the c lassical limit. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scatter ed within the semicircle energy shell while the Green function spectra l density (local spectral density of states) is extended over the whol e shell, but sparse.