Population equations for quantum systems in contact with dissipation mechanisms

Abstract
We discuss the construction of population equations for driven quantum systems in contact with dissipation mechanisms in the limit where the strength of the driving force is sufficiently weak that a suitable Born expansion can be carried out in powers of the coupling constant of the coherent interaction. The Zwanzig projector technique and the application of an appropriate eigenfunction-expansion method due to Weidlich lead to an elegant derivation of population equations. If the decay rates of the irreversible processes allow the application of the Markoff approximation, ordinary first-order differential equations for the level populations can be derived. The transition rates are constructed explicitly in terms of the coherent Liouville operator and the Weidlich eigenfunctions.