J. Phys. I France 4 (1994) 623-628
A matrix ensemble with a preferential basis and its application to disordered metals and insulatorsJean-Louis Pichard1 and Boris Shapiro1, 2
1 C.E.A., Service de Physique de l'Etat Condensé, Centre d'Études de Saclay, 91191 Gif-surYvette Cédex, France
2 Department of Physics, Technion - Israel Institute of Technology, 32000 Haifa, Israel
(Received 28 February 1994, accepted 1 March 1944)
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.
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