General theory of the decoherence effect in quantum mechanics

The decoherence effect, which may be held responsible for the vanishing of macroscopic quantum interferences, has only been exhibited in special models though it is presumed to be universal (at least when there is a possibility of dissipation). A more general model encompassing the already known ones is proposed in the present work. A master equation for the reduced density operator is established by means of two different methods. A direct method, which is given first, is simple but too specific. A second method relies on the projection method in the theory of irreversible processes. It is in principle very general and not confined to a special model. It shows that decoherence is a typical irreversible process from a theoretical standpoint. The master equation is worked out in detail when there exist convenient, so-called microstable collective observables (for which a criterion is given), selecting a preferred basis in which diagonalization occurs. For macroscopic mechanics, this basis is given by the position coordinates in three-dimensional space of relatively small parts in an object. Previously proposed models, including the quantum diffusion model, are found to be special cases of the present theory.