Complex Time Evolution of Open Quantum Systems

We combine, in a single set-up,the complex time parametrization in path integration, and the closed time formalism of non-equilibrium field theories to produce a compact representation of the time evolution of the reduced density matrix. In this framework we introduce a cluster-type expansion that facilitates perturbative and non-perturbative calculations in the realm of open quantum systems. The technical details of some very simple examples are discussed.