Reduced dynamics in the independent oscillator model: exact versus Born–Markov approximation

We derive the formal, exact reduced dynamics for the independent oscillator model in the rotating wave approximation at zero and finite temperature. We show that the traditional form of the Born–Markov approximation is valid beyond this limit, the effect of higher-order contributions being encapsulated into three time-dependent coefficients directly related to the time-dependent mean photon number, and two orthogonal field quadratures. A suggestion on how these coefficients can be measured in currently used optical cavities is given.