Universality of S-matrix correlations for deterministic plus random Hamiltonians

Abstract

We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show that, in the limit of infinite matrix size of the Hamiltonian, correlation functions of S-matrix elements are universal on the scale of the local mean level spacing: the dependence of the deterministic part enters into these correlation functions only through the average S-matrix and the average level density. This statement applies to each of the three symmetry classes (orthogonal, unitary, and symplectic).