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The quantum dynamics of a low-dimensional system in contact with a large butfinite harmonic bath is theoretically investigated by coarse-graining the bathinto a reduced set of effective energy states. In this model, the couplingsbetween the system and the bath are obtained from the statistical average overthe discrete, degenerate effective states. Our model is aimed at intermediatebath sizes in which non-Markovian processes and energy transfer between thebath and the main system are important. The method is applied to a model systemof a Morse oscillator coupled to 40 harmonic modes. The results are found to bein excellent agreement with the direct quantum dynamics simulations ofBouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a muchlower computational cost. Extension to larger baths is discussed in comparisonto the time-convolutionless method. We also extend this study to the case of amicrocanonical bath with finite initial internal energies. The computationalefficiency and convergence properties of the effective bath states model withrespect to relevant parameters are also discussed.

Modeling the dynamics of quantum systems coupled to large dimensional baths using effective energy states