  We study transport equations for quantum many-particle systems in terms of
correlations by applying the general formalism developed in an earlier paper to
exactly soluble electron-phonon models. The one-dimensional models considered
are the polaron model with a linear energy dispersion for the electrons and a
finite number of electrons and the same model including a Fermi sea
(Tomonaga-Luttinger model). The inclusion of two-particle correlations shows a
significant and systematic improvement in comparison with the usual
non-Markovian equations in Born approximation. For example, the improved
equations take into account the renormalization of the propagation by the
self-energies to second order in the coupling.
