On a possible definition of the moving preferred basis

There are many formalisms to describe quantum decoherence. However, many of them give a non general and ad hoc definition of "pointer basis" or "moving preferred basis", and this fact is a problem for the decoherence program. In this paper we will consider quantum systems under a general theoretical framework for decoherence and present a tentative very general definition of the moving preferred basis. which is implemented in a well known open system model. The obtained decoherence and the relaxation times are defined and compared with those of this model.