Density Operator and Multitime Correlation Functions for Open Systems

We describe the dynamics of an open system $\mathcal{S}$ in terms of a nonunitary time evolution operator. The latter is defined to solve the generalized master equation for the density operator of $\mathcal{S}$ as obtained using Zwanzig's projector technique. Multitime correlation functions of observables of $\mathcal{S}$ are expressed in terms of this time evolution operator. Our results generalize well-known fluctuation dissipation (or regression) theorems valid for Markovian motions of open systems. Moreover, they can be used to combine density-operator and Green's-function methods in dealing with open systems. As an example we treat the retarded electron-electron interaction in superconductors.