Timescales for decoherence and dissipation: reasons for the success of master equations

Abstract

A perturbative treatment of reduced density operators of quantum subsystems is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic expressions for linear entropy (a measure of purity loss, and in some cases of coherence loss) and for subsystem's energy variations (dissipation) are given. Application to electromagnetic field superposition states in a dissipative cavity is performed. Evaluation of typical field and reservoir time scales ($\tau_{F}$ and $\tau_{R}$) show that even for small temperatures they are very different. We also indicate the condition on the cutoff temperature above which the decoupling assumption is quantitatively justified.