Few-particle quantum dynamics---comparing Nonequilibrium Green's functions with the generalized Kadanoff-Baym ansatz to density operator theory

TL;DR

This paper compares two theoretical frameworks, NEGF and density operator theory, for describing few-particle quantum dynamics out of equilibrium, highlighting their similarities, differences, and the open questions in their correspondence.

Contribution

It analyzes the relationship between NEGF and density operator approaches, clarifying their connections and differences in few-particle quantum dynamics.

Findings

Both approaches use hierarchy equations (BBGKY and MS)

Similar approximations are used to decouple hierarchies

Open questions remain about their correspondence

Abstract

The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green's functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations---the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green's functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open.