Comparison between the rotating wave and Feynman-Vernon system-reservoir couplings in the non-Markovian regime

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.