A many-body approach to transport in quantum systems: From the transient regime to the stationary state

TL;DR

This paper reviews the non-equilibrium Green's function (NEGF) formalism for studying time-dependent correlated quantum transport in nano-systems, covering theoretical foundations, interaction effects, and diverse applications from transient to steady states.

Contribution

It provides a comprehensive modern introduction to NEGF, including diagrammatic interaction techniques and non-perturbative bath coupling methods, with illustrative examples for complex quantum systems.

Findings

NEGF formalism unifies treatment of interactions, drives, and baths.

Reduction to known quantum transport formulas in special limits.

Application to diverse systems like topological superconductors and molecular junctions.

Abstract

We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive - encompassing pump-probe scenarios as well as driven quantum systems - we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.