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Decoherence in composite quantum open systems: the effectiveness of unstable degrees of freedom

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