Decoherence theory composite system

Also crucial is the following observation relative to the elements of a pointer basis (which is also an eigenbasis of As) are robust [15,16]. Physically, it means that, once effected, the decoherence will keep the states of a pointer basis effectively intact in the course of the unitary evolution of the composite system S + E. This robustness of certain system s states is crucial for the macroscopic context of the decoherence theory. Particularly, it means that the decoherence effect gives rise to both, existence and maintenance of states of a pointer basis — that is, the relevance of the superselection rules — of an open system in the course of the unitary evolution of the combined system S + E. In other words, the decoherence effect tends to freeze the open system s dynamics as defined by the decomposition (9.11). The decoherence time To is usually very short, including the mesoscopic systems such as certain macromolecules [12]. It is therefore not for surprise that the decoherence effect has been observed in the quite controlled circumstances only recently [12,17,18]. 

Physically, the task (b) refers to the nonstationary state of the composite system that is induced by the external action (point (ii) of Section II.B). At the first sight, these two tasks might seem formidable. Fortunately enough, there is a quantum-mechanical theory fulfilling these tasks — the decoherence theory. 

We keep in mind the requirements of Section 11. Then, with respect to the experience with the decoherence theory (Section IV), we call for the rather general, hopefully realistic assumptions about the composite system, that is, about the interactions in the composite systems — (9.20) and (9.25). Particularly, we assume ... 

We essentially make a couple of plausible assumptions or interpretations of the phenomenological data which allow the natural accounting for the decoherence effect in the composite system conformation + environment. These assumptions are worth repeating. First, we assume that every stationary state of the composite system — that is characterized by the constant values of the system s parameters — is characterized by the same land of interaction in the composite system (cf. (9.20)). Second, we assume that the external action — eventually giving rise to the conformational transitions — substantially change the kind of interaction in the (new) composite system (cf. (9.25)). It is a matter of the general decoherence theory straightforwardly to prove the final result (9.33), as well as (9.35) [7,14-16,19]. 

---