  In this article we extend the results presented in Ref. [Phys. Rev. A 76,
032101 (2007)] to treat quantitatively the effects of reservoirs at finite
temperature in a bosonic dissipative network: a chain of coupled harmonic
oscillators whichever its topology, i.e., whichever the way the oscillators are
coupled together, the strength of their couplings and their natural
frequencies. Starting with the case where distinct reservoirs are considered,
each one coupled to a corresponding oscillator, we also analyze the case where
a common reservoir is assigned to the whole network. Master equations are
derived for both situations and both regimes of weak and strong coupling
strengths between the network oscillators. Solutions of these master equations
are presented through the normal ordered characteristic function. We also
present a technique to estimate the decoherence time of network states by
computing separately the effects of diffusion and the attenuation of the
interference terms of the Wigner function. A detailed analysis of the diffusion
mechanism is also presented through the evolution of the Wigner function. The
interesting collective diffusion effects are discussed and applied to the
analysis of decoherence of a class of network states. Finally, the entropy and
the entanglement of a pure bipartite system are discussed.
