  Random matrix theory is used to represent generic loss of coherence of a
fixed central system coupled to a quantum-chaotic environment, represented by a
random matrix ensemble, via random interactions. We study the average density
matrix arising from the ensemble induced, in contrast to previous studies where
the average values of purity, concurrence, and entropy were considered; we
further discuss when one or the other approach is relevant. The two approaches
agree in the limit of large environments. Analytic results for the average
density matrix and its purity are presented in linear response approximation.
The two-qubit system is analysed, mainly numerically, in more detail.
