Electron Transfer Methods in Open Systems

Utilization of electron transfer methods for description of quantum transport is popular due to simplicity of the formulation and its ability to account for basic physics of electron exchange between the system and baths. At the same time, the necessity to go beyond simple golden rule-type expressions for rates was indicated in the literature and ad hoc formulations were proposed. Similarly, kinetic schemes for quantum transport beyond the usual second-order Lindblad/Redfield considerations were discussed. Here we utilize recently introduced the nonequilibrium Hubbard Green's function diagrammatic technique to analyze the construction of rates in open systems. We show that previous considerations for rates of second and fourth order can be obtained as a particular case of zero- and second-order Green's function diagrammatic series with bare diagrams. We discuss limitations of previous considerations, stress advantages of the Hubbard Green's function approach in constructing the rates, and indicate that standard dressing of the diagrams is a natural way to account for additional baths/degrees of freedom in the formulation of generalized expressions for the rates.