  The purpose of these notes is to give a fairly narrow but thorough
introduction to the spectral analysis of Hamiltonians and standard Liouvilleans
describing finite dimensional small systems linearly coupled to a scalar
massless field or reservoir. The Hamiltonians describe the system at zero
temperature, and the standard Liouvillean implements unitarily the dynamics of
the system at positive temperature.
  We focus our attention on results valid at arbitrary coupling strength and
whose proofs are purely operator theoretic, i.e. for the standard Liouvillean
does not make use of the underlying modular structure. This means that
important structure results at positive temperature that does not seem to have
a purely operator theoretic proof will only be reviewed.
