Solving the Kadanoff-Baym equations for inhomogenous systems: Application to atoms and molecules

TL;DR

This paper presents a method for solving the Kadanoff-Baym equations to simulate electron dynamics in atoms and molecules, enabling accurate spectral and excitation calculations in non-perturbative fields.

Contribution

The authors implement time-propagation of non-equilibrium Green functions for inhomogeneous systems, demonstrating its effectiveness for spectral and excitation energy computations.

Findings

Successful time-propagation for spectral functions

Accurate description of correlated electron dynamics

Calculation of charge-neutral excitation energies

Abstract

We have implemented time-propagation of the non-equilibrium Green function for atoms and molecules, by solving the Kadanoff-Baym equations within a conserving self-energy approximation. We here demonstrate the usefulnes of time-propagation for calculating spectral functions and for describing the correlated electron dynamics in a non-perturbative electric field. We also demonstrate the use of time-propagation as a method for calculating charge-neutral excitation energies, equivalent to highly advanced solutions of the Bethe-Salpeter equation.