# Electron Transfer Methods in Open Systems

## TL;DR

This paper introduces a nonequilibrium Hubbard Green's functions diagrammatic technique to improve the construction of electron transfer rates in open quantum systems, surpassing traditional second and fourth order methods.

## Contribution

It presents a novel diagrammatic approach that generalizes rate calculations and incorporates additional baths or degrees of freedom naturally.

## Key findings

- Previous rate calculations are special cases of the new diagrammatic series.
- The Hubbard Green's function approach offers advantages over traditional methods.
- Standard diagram dressing allows for inclusion of more complex system-bath interactions.

## Abstract

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 system and baths. At the same time, 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 usual second order Lindblad/Redfield considerations were discussed. Here we utilize recently introduced by us nonequilibrium Hubbard Green's functions diagrammatic technique to analyze 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 when formulating generalized expressions for the rates.