  The transition from arbitrary to chaotic fluctuation properties in quantum
systems is studied in a random matrix model. It is assumed that the Hamiltonian
can be written as the sum of an arbitrary and a chaos producing part. The
Gaussian ensembles are used to model the chaotic part. A closed integral
representation for all correlations in the case of broken time reversal
invariance is derived by employing supersymmetry and the graded eigenvalue
method. In particular, the two level correlation function is expressed as a
double integral. For a correlation index, exact diffusion equations are derived
for all three universality classes which describe the transition to the chaotic
regime from arbitrary initial conditions. As an application, the transition
from Poisson regularity to chaos is discussed. The two level correlation
function becomes a double integral for all values of the transition parameter.

Condensed Matter