ENVIRONMENT-INDUCED DECOHERENCE, CLASSICALITY, AND CONSISTENCY OF QUANTUM HISTORIES

We prove that for an open system, in the Markovian regime, it is alway s possible to construct an infinite number of nontrivial sets of histo ries that exactly satisfy the probability sum rules. In spite Of being perfectly consistent, these sets manifest a very nonclassical behavio r: they are quite unstable under the addition of an extra instant to t he list of times defining the history. To eliminate this feature-the i mplications of which we discuss-and to achieve the stability that char acterizes the quasiclassical domain, it is necessary to separate the i nstants which define the history by time intervals significantly large r than the typical decoherence time. In this case environment induced superselection is very effective. The quasiclassical domain is defined by predictably evolving perferred states, ''pointer projectors,'' whi ch give rise to consistent preferred sets of histories.