Superselection rules

In this limit, therefore, the different ground states generate separate Hilbert spaces, and transitions among them are forbidden. A superselection rule [128] is said to insulate one ground state from another. A superselection rule operates between subspaces if there are neither spontaneous transitions between their state vectors and if, in addition, there are no measurable quantities with finite matrix elements between their state vectors. 

The infinite potential barrier, shown schematically in figure 10 corresponds to a superselection rule that operates below the critical temperature [133]. Above the critical temperature the quantum-mechanical superposition principle applies, but below that temperature the system behaves classically. The system bifurcates spontaneously at the critical point. The bifurcation, like second-order phase transformation is caused by some interaction that becomes dominant at that point. In the case of chemical reactions the interaction leads to the rearrangement of chemical bonds. The essential difference between chemical reaction and second-order phase transition is therefore epitomized by the formation of chemically different species rather than different states of aggregation, when the symmetry is spontaneously broken at a critical point. 

Pfeifer, P. Chiral Molecules - A Superselection Rule Induced by the Radiation Field (Doctoral Thesis, Swiss Federal Inst, of Techn., Diss. ETH No. 6551), 1980... 

P. Pfeifer, Chiral Molecules—a Superselection Rule Induced by the Radiation Field, Thesis 6551, ok Gotthard S + D AG, ETH-Ziirich, Zurich, 1980. 

Diffraction experiments are carried out by thermal neutrons and with observation times of 10 13 s or more. These experiments indicate that H - H entanglement survives over an unusually long time in this particular compound. The reason for the long decoherence time was discussed in Ref. [Fillaux 1998] as a result of restricted coupling of the H - H dimers to the KII( () >, environment caused by specific fermion / boson superselection rules. 

Amann, A, 1990. "Chirality A Superselection Rule Generated by the Molecular Environment " Journal of Mathematical Chemistry, 6 1-15. 

A. Amann, Chirality A superselection rule generated by the molecular environment, J. Math. Chem. 6 (1991) 1-15. 

A word of caution is worth saying. Sometimes, some physically different processes or effects are misidentified or misinterpreted as decoherence. Below, we give a precise definition of decoherence, that is, of the decoherence-induced superselection rules ect [14], which we refer to as decoherence. ... 

More precisely The matrix representation of pg in the basis diagonal form, thus giving rise to the effective superselection rules [ 14,15] for the open system that is described by the orthogonal decomposition of the system s Hilbert state ... 

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]. 

Finally, in principle, certain external actions on the composite system can effect in breaking the superselection rules, that is, of the decoherence effect. Actually, for certain interactions with another external system E, if one may write ... 

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