  The effect induced by an environment on a composite quantum system is
studied. The model considers the composite system as comprised by a subsystem A
coupled to a subsystem B which is also coupled to an external environment. We
study all possible four combinations of subsystems A and B made up with a
harmonic oscillator and an upside down oscillator. We analyzed the decoherence
suffered by subsystem A due to an effective environment composed by subsystem B
and the external reservoir. In all the cases we found that subsystem A
decoheres even though it interacts with the environment only through its sole
coupling to B. However, the effectiveness of the diffusion depends on the
unstable nature of subsystem A and B. Therefore, the role of this degree of
freedom in the effective environment is analyzed in detail
