In this work, the Dyson's equation formalism is outlined and applied toseveral open quantum systems. These systems are composed of a core,quantum-mechanical set of discrete states and several continua, representing macroscopic systems. The macroscopic systems introducedecoherence, as well as allowing the total particlenumber in the system to change.Dyson's equation, an expansion in terms of proper self-energy terms, isderived. The hybridization of two quantum levelsis reproduced in this formalism, and it is shown that decoherence followsnaturally when one of the levels is replaced by a continuum.The work considers three physical systems in detail. The first,quantum dots coupled in series with two leads, is presented in a realistic two-level model. Dyson's equation is used to account for the leads exactly to all ordersin perturbation theory, and the time dynamics of a single electron in the dotsis calculated. It is shown that decoherence from the leads damps the coherentRabi oscillations of the electron. Several regimes of physical interest areconsidered, and it is shown that the difference in couplings of the two leadsplays a central role in the decoherence processes.The second system relates to the decay-out ofsuperdeformed nuclei. In this case, decoherence is provided by coupling to theelectromagnetic field. Two, three, and infinite-level models are consideredwithin the discrete system. It is shown that the two-level model is usuallysufficient to describe decay-out for the classic regions of nuclearsuperdeformation. Furthermore, a statistical model for the normal-deformedstates allows extraction of parameters of interest to nuclear structure fromthe two-level model. An explanation for the universality of decayprofiles is also given in that model.The final system is a proposed small molecular transistor. TheQuantum Interference Effect Transistor is based on a single monocyclic aromatic annulene molecule, with twoleads arranged in the meta configuration. This device is shown to be completely opaque to charge carriers, due to destructive interference. Thiscoherence effect can be tunably broken by introducing new paths with a real orimaginary self-energy, and an excellentmolecular transistor is the result.