The RPA description of the quantum damped harmonic oscillator

Abstract

We have developed a microscopic, time reversible model which behaves like a damped harmonic oscillator for times short compared to the system's Poincaré time. The model assumes an RPA description of initial collective states within a restricted subspace, thentraces their time evolution when an additional subspace (the reservoir) is coupled to the restricted subspace. The assumption that this time evolution is also governed by RPA dynamics is utilized. The evolution of packets initialized as the shifted eigenstates of an undamped oscillator of arbitrary frequency (different from the frequency of the collective phonon) allows the explicit study of the expectation values and the fluctuations in the collective coordinates. In all cases, the fluctuations decay to their zero point values. Due to the decay of the fluctuations, the energy loss rate deviates from Rayleigh's result for classical mechanics. The RPA description contrasts with both the Albrecht and the Kostin descriptions.