AMENDART in Markovian circuit QED

We study the cavity field's and atomic asymptotic mean excitation numbers due to anti-rotating term (AMENDART) in the circuit Quantum Electrodynamics (circuit QED) system, composed of a two-level atom and a single cavity field mode, subject to Markovian damping and dephasing mechanisms. We show that the AMENDART are above the thermal values, and their behavior is analyzed analytically and numerically for typical parameters in circuit QED implementations described by the Rabi Hamiltonian. We point out that "parasitic elements", such as other cavity modes or eventual off-resonant atoms, also contribute substantially to AMENDART.