A MATRIX ENSEMBLE WITH A PREFERENTIAL BASIS AND ITS APPLICATION TO DISORDERED METALS AND INSULATORS

The standard ensembles of random matrices are invariant under change o f basis. In disordered systems, this invariance is broken and deviatio ns from the random matrix theory predictions occur, especially for str ong disorder. We consider a generalization of the standard ensembles w hich includes a preferential basis and which gives rise to a ''screene d'' pairwise interaction between energy levels. As a function of the c onductance g, we qualitatively describe level statistics in the metal, insulator and at the mobility edge. In the unitary case, an exact sol ution of this model is provided by earlier works of Gaudin.