  We consider the time evolution of a quantized field in backgrounds that
violate the vacuum stability (particle-creating backgrounds). Our aim is to
study the exact form of the final quantum state (the density operator at a
final instant of time) that has emerged from a given arbitrary initial state
(from a given arbitrary density operator at the initial time instant) in the
course of the evolution. We find a generating functional that allows us to have
the density operators for any initial state. Averaging over states of a
subsystem of antiparticles (particles), we obtain explicit forms for reduced
density operators for subsystems of particles (antiparticles). Studying
one-particle correlation functions, we establish a one-to-one correspondence
between these functions and the reduced density operators. It is shown that in
the general case a presence of bosons (e.g. gluons) in an initial state
increases the creation rate of the same kind of bosons. We discuss the question
(and its relation to the initial stage of quark-gluon plasma formation) whether
a thermal form of one-particle distribution can appear even if the final state
of the complete system is not a thermal equilibrium. In this respect, we
discuss some cases when a pair creation by an electric-like field can mimic a
one-particle thermal distribution. We apply our technics to some QFT problems
in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric,
and metric. In particular, we study the time and temperature behavior of mean
numbers of created particles provided switching on and off effects of the
external field are negligible. It is shown that at high temperatures and in
slowly varying electric fields the rate of particle creation is essentially
time-dependent.
