Quantum energy decays and decoherence in discrete baths
  The quantum average energy decay and the purity decay are studied for a system particle as a function of the number of constituents of a discrete bath model. The system particle is subjected to two distinct physical situations: the harmonic oscillator (HO) and the Morse potential. The environment (bath) is composed by a {\it finite} number N of uncoupled HOs, characterizing the structured bath, which in the limit $N\to\infty$ is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. For very low values of N the mean energy and purity remain constant in time but starts to decay for intermediate values (10<N<20), where two distinct time regimes are observed: two exponential decays for relatively short times and a power-law decay for larger times. In this interval of N decoherence occurs for short times and a non-Markovian dynamics is expected for larger times. When $N$ increases, energy and coherence decay very fast and a Markovian dynamics is expected to occur. Wave packet dynamics is used to determine the evolution of the particle inside the system potentials. 
M. D. Galiceanu and M. W. Beims and W. Strunz
quant-ph