  This paper deals with the dissipative dynamics of a quantum harmonic
oscillator interacting with a bosonic reservoir. The Master Equations based on
the Rotating Wave and on the Feynman-Vernon system--reservoir couplings are
compared highlighting differences and analogies. We discuss quantitatively and
qualitatively the conditions under which the counter rotating terms can be
neglected. By comparing the analytic solution of the heating function relative
to the two different coupling models we conclude that, even in the weak
coupling limit, the counter rotating terms give rise to a significant
contribution in the non--Markovian short time regime. The main result of this
paper is that such a contribution is actually experimentally measurable and
thus relevant for a correct description of the system dynamics.
