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There are many formalisms to describe quantum decoherence. However, many ofthem give a non general and ad hoc definition of "pointer basis" or "movingpreferred basis", and this fact is a problem for the decoherence program. Inthis paper we will consider quantum systems under a general theoreticalframework for decoherence and we will present a tentative definition of themoving preferred basis. These ideas are implemented in a well-known open systemmodel. The obtained decoherence and the relaxation times are defined andcompared with those of the literature for the Lee- Friedrichs model.

Non-Hermitian Hamiltonians in decoherence and equilibrium theory