Decoherence induced by a composite environment

We study the decoherence induced by the environment over a composite quantum system, comprising two coupled subsystems A and B, which may be a harmonic or an upside-down oscillators. We analyze the case in which the B-subsystem is in direct interaction with a thermal bath, while the other remains isolated from the huge reservoir. We compare the results concerning the decoherence suffered by the A-subsystem.