Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions

TL;DR

This paper develops a superoperator nonequilibrium Green's function framework in Liouville space for quantum many-body systems, simplifying calculations of dynamical responses and transport properties in open quantum junctions.

Contribution

It introduces a superoperator algebra approach in Liouville space, enabling real-time calculations of observables without the complex time-loop formalism.

Findings

Derived expressions for charge densities and currents in real time.

Applied the theory to compute current fluctuations and electroluminescence.

Simplified the physical interpretation of nonequilibrium Green's functions.

Abstract

Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of superoperator nonequilibrium Green's functions (SNGF), rather than the artificial time-loop required in Schwinger's Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed.