Quantum Dissipation in Rotating Wave Approximation

We study composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution. To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for transition amplitudes of the dissipative system with the help of the perturbation analysis.