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 of basis. In disordered systems, this invariance is broken and deviations from the random matrix theory predictions occur, especially for strong disorder. We consider a generalization of the standard ensembles which includes a preferential basis and which gives rise to a "screened" pairwise interaction between energy levels. As a function of the conductance g, we qualitatively describe level statistics in the metal, insulator and at the mobility edge. In the unitary case, an exact solution of this model is provided by earlier works of Gaudin.