  In the context of the mixing dynamical systems we present a derivation of the
Gaussian ensembles distributions from mixing quantum systems having a classical
analog that is mixing. We find that mixing factorization property is satisfied
for the mixing quantum systems expressed as a factorization of quantum mean
values. For the case of the kicked rotator and in its fully chaotic regime, the
factorization property links decoherence by dephasing with Gaussian ensembles
in terms of the weak limit, interpreted as a decohered state. Moreover, a
discussion about the connection between random matrix theory and quantum
chaotic systems, based on some attempts made in previous works and from the
viewpoint of the mixing quantum systems, is presented.
