  The time evolution of anharmonic molecular wave packets is investigated under
the influence of the environment consisting of harmonic oscillators. These
oscillators represent photon or phonon modes and assumed to be in thermal
equilibrium. Our model explicitly incorporates the fact that in the case of a
nonequidistant spectrum the rates of the environment induced transitions are
different for each transition. The nonunitary time evolution is visualized by
the aid of the Wigner function related to the vibrational state of the
molecule. The time scale of decoherence is much shorter than that of
dissipation, and gives rise to states which are mixtures of localized states
along the phase space orbit of the corresponding classical particle. This
behavior is to a large extent independent of the coupling strength, the
temperature of the environment and also of the initial state.
