Time-propagation of the Kadanoff-Baym equations for inhomogeneous systems

TL;DR

This paper presents a new time propagation scheme for the Kadanoff-Baym equations, enabling the simulation of inhomogeneous many-body systems under time-dependent external fields while preserving conservation laws.

Contribution

The authors develop a general time propagation method for the Kadanoff-Baym equations applicable to inhomogeneous systems with nonperturbative external fields and perturbative many-body interactions.

Findings

Effective scheme for inhomogeneous systems

Incorporates various self-energy approximations

Ensures conservation laws are satisfied

Abstract

We have developed a time propagation scheme for the Kadanoff-Baym equations for general inhomogeneous systems. These equations describe the time evolution of the nonequilibrium Green function for interacting many-body systems in the presence of time-dependent external fields. The external fields are treated nonperturbatively whereas the many-body interactions are incorporated perturbatively using Phi-derivable self-energy approximations that guarantee the satisfaction of the macroscopic conservation laws of the system. These approximations are discussed in detail for the time-dependent Hartree-Fock, the second Born and the GW approximation.