Nonequilibrium Green's function approach to the pair distribution function of quantum many-body systems out of equilibrium

TL;DR

This paper develops a Green's function-based method to calculate the pair distribution function in quantum many-body systems out of equilibrium, incorporating initial correlations and extending previous theories.

Contribution

It introduces a Green's function approach to derive the PDF for out-of-equilibrium quantum systems, generalizing earlier density matrix methods.

Findings

Derived an expression for the PDF using single-particle Green's functions.

Includes initial correlations in the PDF calculation.

Provides explicit formulas within the second Born approximation.

Abstract

The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green's functions---the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane---for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.