  In the framework of quantum open systems, that is, simple quantum systems
coupled to quantum baths, our aim is to characterize those actions of the
quantum environment which give rise to dynamics dictated by classical noises.
First, we consider the discrete time scheme, through the model of repeated
quantum interactions. We explore those unitary interactions which make the
environment acting as if it were a classical noise, that is, dynamics which
ought to random walks on the unitary group of the small system. We show that
this characterization is intimately related to the notion of complex obtuse
random variables. These particular random variables have an associated 3-tensor
whose symmetries make it diagonalizable in some orthonormal basis. We show how
this diagonalisation entirely describes the behavior of the random walk
associated to the action of the environment. In particular this 3-tensor and
its diagonalization characterize the behavior of the continuous-time limits;
they characterize the directions along which the limit process is of diffusive
or of Poisson nature.
