We adopt the general formalism, which was developed in Paper I(arXiv:0708.1233) to analyze the evolution of a quantized time-dependentoscillator, to address several questions in the context of quantum field theoryin time dependent external backgrounds. In particular, we study the question ofemergence of classicality in terms of the phase space evolution and itsrelation to particle production, and clarify some conceptual issues. Weconsider a quantized scalar field evolving in a constant electric field and inFRW spacetimes which illustrate the two extreme cases of late time adiabaticand highly non-adiabatic evolution. Using the time-dependent generalizations ofvarious quantities like particle number density, effective Lagrangian etc.introduced in Paper I, we contrast the evolution in these two limits bringingout key differences between the Schwinger effect and evolution in the de Sitterbackground. Further, our examples suggest that the notion of classicality ismultifaceted and any one single criterion may not have universal applicability.For example, the peaking of the phase space Wigner distribution on theclassical trajectory \emph{alone} does not imply transition to classicalbehavior. An analysis of the behavior of the \emph{classicality parameter},which was introduced in Paper I, leads to the conclusion that strong particleproduction is necessary for the quantum state to become highly correlated inphase space at late times.
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