CORRELATIONS OF NEARBY LEVELS INDUCED BY A RANDOM POTENTIAL

We consider a Hamiltonian H which is the sum of a deterministic part H -0 and of a random potential V. For finite N x N matrices, following a method introduced by Kazakov, we derive a representation of the corre lation functions in terms of contour integrals over a finite number of variables. This allows one to analyse the level correlations, whereas the standard methods of random matrix theory, such as the method of o rthogonal polynomials, are not available for such cases. At short dist ance we recover, for an arbitrary H-0, an oscillating behavior for the connected two-level correlation.