Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Projection operators - non-equilibrium Green functions approach to quantum transport

Maicol A. Ochoa, Michael Galperin, Mark A. Ratner

Published Mar 5, 2014• 0 citations
OpenAlex

Related papers

Quantum transport: the Non-Equilibrium Green's Function formalism

WORLD SCIENTIFIC eBooks•Oct 5, 2016•0 citations

A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

Maicol A. Ochoa, Michael Galperin, Mark A. Ratner

We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

arXiv:1406.3315•Journal of Physics Condensed Matter•Oct 16, 2014•8 citations

Density matrix description of non-equilibrium quantum transport

Prasenjit Dutt, Jens Koch, Chung‐Hou Chung +2 more

Bulletin of the American Physical Society•Mar 17, 2010•0 citations

Multi-mode Floquet NEGF method for driven quantum transport

Vahid Mosallanejad, Wenjie Dou

We present a non-perturbative Floquet-based non-equilibrium Green's function (NEGF) method to study electron transport in a quantum system driven simultaneously by multiple independent terms (multi-mode). We first derive the two-mode Floquet NEGF based on two-step transformations of the retarded-advanced Green's function from the Kadanoff-Baym equation. This derivation proceeds by elaborating on the expectation values of the number and current operators. The two-mode Floquet NEGF is then extended to cases with multiple drivings. The method is tested by investigating current suppression in the presence of two drivings. We show that an extra sinusoidal off-diagonal driving can cause substantial modification to the current suppression, provided careful selection of the driving frequency. Consequently, we expect that the established method has broad applications in a wide range of open quantum systems driven by complicated drivings.

arXiv:2605.19296•May 19, 2026•0 citations

Projection operator approach to transport in complex single-particle quantum systems

Robin Steinigeweg, Jochen Gemmer B, Heinz‐Peter Breuer +1 more

arXiv:0903.5427•The European Physical Journal B•Apr 25, 2009•6 citations

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

M Ridley, N. Walter Talarico, Daniel Karlsson +2 more

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.

arXiv:2201.02646•Journal of Physics A Mathematical and Theoretical•May 18, 2022•32 citations
We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.
We present a non-perturbative Floquet-based non-equilibrium Green's function (NEGF) method to study electron transport in a quantum system driven simultaneously by multiple independent terms (multi-mode). We first derive the two-mode Floquet NEGF based on two-step transformations of the retarded-advanced Green's function from the Kadanoff-Baym equation. This derivation proceeds by elaborating on the expectation values of the number and current operators. The two-mode Floquet NEGF is then extended to cases with multiple drivings. The method is tested by investigating current suppression in the presence of two drivings. We show that an extra sinusoidal off-diagonal driving can cause substantial modification to the current suppression, provided careful selection of the driving frequency. Consequently, we expect that the established method has broad applications in a wide range of open quantum systems driven by complicated drivings.
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.