  We address the question whether observables of an exactly solvable model of
electrons coupled to (optical) phonons relax into large time stationary state
values and investigate if the asymptotic expectation values can be computed
using a stationary density matrix. Two initial nonequilibrium situations are
considered. A sudden quench of the electron-phonon coupling, starting from the
noninteracting canonical equilibrium at temperature T in the electron as well
as in the phonon subsystems, leads to a rather simple dynamics. A richer time
evolution emerges if the initial state is taken as the product of the phonon
vacuum and the filled Fermi sea supplemented by a highly excited additional
electron. Our model has a natural set of constants of motion, with as many
elements as degrees of freedom. In accordance with earlier studies of such type
of models we find that expectation values which become stationary can be
described by the density matrix of a generalized Gibbs ensemble which differs
from that of a canonical ensemble. For the model at hand it appears to be
evident that the eigenmode occupancy operators should be used in the
construction of the stationary density matrix.
