  We study the problem of the basis of an open quantum system, under a quantum
chaotic environment, which is preferred in view of its stationary reduced
density matrix (RDM), that is, the basis in which the stationary RDM is
diagonal. It is shown that, under an initial condition composed of sufficiently
many energy eigenstates of the total system, such a basis is given by the
eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of
large Hilbert space of the environment. Here, the renormalized self-Hamiltonian
is given by the unperturbed self-Hamiltonian plus a certain average of the
interaction Hamiltonian over the environmental degrees of freedom. Numerical
simulations, performed in two models, both with the kicked rotor as the
environment, give results consistent with the above analytical predictions for
the limit of large environment.
