  We explore the influence of external perturbations on the energy levels of a
Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian
matrices. By deriving the joint distribution function of eigenvalues, we obtain
the (n,m)-point parametric correlation function of the initial and final
density of states for perturbations of arbitrary rank and strength. A further
generalization of these results allows for the incorporation of short-range
spatial correlations in diffusive as well as ballistic chaotic structures.
