  The quantum dynamics of a low-dimensional system in contact with a large but
finite harmonic bath is theoretically investigated by coarse-graining the bath
into a reduced set of effective energy states. In this model, the couplings
between the system and the bath are obtained from the statistical average over
the discrete, degenerate effective states. Our model is aimed at intermediate
bath sizes in which non-Markovian processes and energy transfer between the
bath and the main system are important. The method is applied to a model system
of a Morse oscillator coupled to 40 harmonic modes. The results are found to be
in excellent agreement with the direct quantum dynamics simulations of
Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much
lower computational cost. Extension to larger baths is discussed in comparison
to the time-convolutionless method. We also extend this study to the case of a
microcanonical bath with finite initial internal energies. The computational
efficiency and convergence properties of the effective bath states model with
respect to relevant parameters are also discussed.
