A matrix ensemble with a preferential basis and its application to disordered metals and insulators

Jean-Louis Pichard; Boris Shapiro

doi:doi:10.1051/jp1:1994165

Numéro		J. Phys. I France Volume 4, Numéro 5, May 1994


Page(s)		623 - 628
DOI		https://doi.org/10.1051/jp1:1994165

DOI: 10.1051/jp1:1994165
J. Phys. I France 4 (1994) 623-628

Short Communication

A matrix ensemble with a preferential basis and its application to disordered metals and insulators

Jean-Louis Pichard¹ and Boris Shapiro^{1, 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)

Abstract
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.