Comments on a semigroup formalism for the description of phase and population relaxation processes

Population and phase relaxation in two molecular models is studied. The analysis is based on recent work by Lindblad, in which the time evolution of an N-level quantum system is described using the coresponding generator of a completely positive semigroup. One of the models studied corresponds to a diatomic molecule in a dense medium. New results are obtained for the influence of two quantum transitions on population and phase relaxation. The other model studied corresponds to the case of exchange dephasing in a polyatomic molecule embedded in a dense medium. The formalism permits inclusion of coupling terms neglected by Harris, Shelby, and Cornelius; it is shown that inclusion of these terms leads to a rich range of line shapes, which information is not available from the approximation used by Harris et al.