Kadanoff-Baym Equations with Initial Correlations

TL;DR

This paper generalizes the Kadanoff-Baym equations to include arbitrary initial correlations, overcoming the common assumption of their weakening, and demonstrates the impact through numerical analysis.

Contribution

The authors derive a more general form of the Kadanoff-Baym equations that incorporates initial correlations without the weakening assumption, using functional derivatives.

Findings

Inclusion of initial correlations affects short-time dynamics.

The additional collision integral is damped after several collisions.

Numerical results show the significance of initial correlations.

Abstract

The Kadanoff-Baym equations (KBE) are usually derived under the assumption of the weakening of initial correlations (Bogolyubov's condition) and, therefore, fail to correctly describe the short time behavior. We demonstrate that this assumption is not necessary. Using functional derivatives techniques, we present a straightforward generalization of the KBE which allows to include arbitrary initial correlations and which is more general than previous derivations. As a result, an additional collision integral is obtained which is being damped out after a few collisions. Our results are complemented with numerical investigations showing the effect of initial correlations.