  We calculate the reduced density matrix for a system of coupled harmonic
oscillators in a bosonic heat bath using the Born-Markov approximation and show
that the expectation values of position and momentum evolve like classical
quantities. We consider the cases where every oscillator is coupled to its own
reservoir and where all oscillators are coupled to the same heat bath, pointing
out the differences between these two models. In particular, for systems
coupled to a common reservoir, we present an uncommon dissipation mechanism,
which disappears, when the dynamics of the system are gouverned by the low
frequency modes of the environment (Caldeira-Leggett limit). We also address
the interesting phenomenon of reservoir-induced interactions.
