Universal correlations for deterministic plus random Hamiltonians

Abstract

We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $φ$. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed H0 and for a class of probability distribution P$(φ)$ of the random potential. We find a compact representation of the correlation function. From this representation one obtains readily the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both H0 and P($φ$).