A formalism for minimal irreversible quantum mechanics is extended from pure states to mixed states. In the latter case the problem of their diagonal singularity is explained and solved. In addition to the pure and mixed states of the usual approach, more general states are obtained. The Friedrichs model is studied. Decoherence is found and decoherence characteristic times are computed. ͓S1050-2947͑98͒03505-7͔PACS number͑s͒: 03.65.Ϫw

It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable states that vanish when t → ∞. These "Gamov vectors" have zero norm, in such a way that the norm and the energy of the physical states remain constant. The evolution operator has no inverse, showing that we are really dealing with a time-asymmetric theory. Using Friedrichs model reasonable physical results are obtained, e. g. : the remaining of an unstable decaying state reappears, in the continuous spectrum of the model, with its primitive energy.•PACS Nrs. 05.20-y, 03.65. BZ, 05.30-d.•

Considering quantum states as functionals acting on observables to give their mean values, it is possible to deal with quantum systems with continuous spectrum, generalizing the concept of trace. Generalized observables and states are defined for a quantum oscillator linearly coupled to a scalar field, and the analytic expression for time evolution is obtained. The ''final'' state (t→ϱ) is presented as a weak limit. Finite and infinite numbers of excited modes of the field are considered. ͓S1063-651X͑98͒09004-7͔

Decoherence and the approach to the classical final limit are studied in two similar cases: the Mott and the Cosmological problems.

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A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian's spectrum. Several decoherence times are estimated: 10 −13 − 10 −15 s for microscopic systems, and 10 −37 − 10 −39 s for macroscopic bodies. For the particular case of a thermal bath, our results agree with those obtained by the einselection (environment-induced decoherence) approach. PACS number(s) 03.65.Bz

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Given the impressive success of environment-induced decoherence (EID), nowadays no interpretation of quantum mechanics can ignore its results. The modal-Hamiltonian interpretation (MHI) has proved to be effective for solving several interpretative problems but, since its actualization rule applies to closed systems, it seems to stand at odds of EID. The purpose of this paper is to show that this is not the case: the states einselected by the interaction with the environment according to EID (the elements of the "pointer basis") are the eigenvectors of an actualvalued observable belonging to the preferred context selected by the MHI.