Random matrix models with additional interactions

Abstract

It has been argued that, despite remarkable success, existing random matrix theories are not adequate at describing disordered conductors in the metallic regime, due to the presence of certain two-body interactions in the effective Hamiltonian for the eigenvalues, in addition to the standard logarithmic interaction that arises entirely from symmetry considerations. We present a new method that allows exact solution of random matrix models with such additional two-body interactions. This should broaden the scope of random matrix models in general.