Hierarchy of times of open optical quantum systems and the role of the effective Hamiltonian in the white noise approximation

The hierarchy of characteristic times naturally justifies the necessity of the transition from the initial “exact” Hamiltonian of an open quantum system and its environment to an approximate effective Hamiltonian for the further use of the Markov approximation and the model of the delta-correlated environment of the open system. The transition to the effective Hamiltonian within the algebraic perturbation theory makes it possible to take into account interference relaxation channels and specific interference of random processes that cannot be detected and are absent in the rotating wave approximation. It has been shown that specific interference in the case of an ensemble of identical quantum oscillators results in a non-Wiener dynamics of the ensemble.