# A Dyson equation for non-equilibrium Green's functions in the partition-free setting

## TL;DR

This paper develops a rigorous Dyson equation framework for non-equilibrium Green's functions in a partition-free setting, enabling precise analysis of quantum transport after bias application.

## Contribution

It introduces a novel Dyson equation formulation for non-equilibrium Green's functions in the partition-free scenario, with a closed-form self-energy expression.

## Key findings

- Rigorous formulation of Dyson equation using Volterra operators
- Closed formula for the interaction self-energy
- Applicable to quantum transport in interacting systems

## Abstract

We consider a small interacting sample coupled to several non-interacting leads. Initially, the system is at thermal equilibrium. At some instant $t_0$ the system is set into the so called partition-free transport scenario by turning on a bias on the leads. Using the theory of Volterra operators we rigorously formulate a Dyson equation for the retarded Green's function and we establish a closed formula for the associated proper interaction self-energy.