Markovian and rotating-wave approximations versus exact solution of damped quantum oscillator

摘要

The system of one harmonic oscillator interacting with a continuum is studied. The problem is solved for two cases: the exact (full) Hamiltonian and the truncated Hamiltonian [the rotating-wave approximation (RWA)]. Comparing these two solutions, we formulate the conditions of the applicability of the RWA. The case in which the solution can be treated as Markovian is also discussed. The conditions for the existence of discrete levels are obtained. It was shown that under certain conditions, nonoscillating terms in the solution, leading to the instability of the whole system, can exist. Such terms cannot be obtained within either the Markovian or the rotating-wave approximation. Two particular cases of coupling are proposed and the results of numerical simulations are discussed.