  There exists the well known approximate expression describing the large time
behaviour of matrix elements of the evolution operator in quantum theory:
<U(t)>=exp(at)+... This expression plays the crucial role in considerations of
problems of quantum decoherence, radiation, decay, scattering theory,
stochastic limit, derivation of master and kinetic equations etc. This
expression was obtained in the Weisskopf-Wigner approximation and in the van
Hove (stochastic) limit. We derive the exact general formula which includes the
higher order corrections to the above approximate expression:
<U(t)>=exp(At+B+C(t)). The constants A and B and the oscillating function C(t)
are computed in perturbation theory. The method of perturbation of spectra and
renormalized wave operators is used. The formula is valid for a general class
of Hamiltonians used in statistical physics and quantum field theory.
