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This paper gives an introduction to the Keldysh formalism, with emphasis on its usefulness in time-dependent density functional theory. In the first part we introduce the Keldysh contour and the one-particle Green function defined on this…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Robert van Leeuwen , Nils Erik Dahlen , Gianluca Stefanucci , Carl-Olof Almbladh , Ulf von Barth

Nonequilibrium electronic transport through a quantum dot coupled to ferromagnetic leads (electrodes) is studied theoretically by the nonequilibrium Green function technique. The system is described by the Anderson model with arbitrary…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 R. Swirkowicz , M. Wilczynski , J. Barnas

We study the effect of spin-orbit interaction and in-plane effective magnetic field on the conductance of a quasi-one-dimensional ballistic electron system. The effective magnetic field includes the externally applied field, as well as the…

Mesoscale and Nanoscale Physics · Physics 2010-10-12 Yuriy V. Pershin , James A. Nesteroff , Vladimir Privman

Recent breakthroughs in quantum-dot circuit-quantum-electrodynamics (circuit-QED) systems are important both from a fundamental perspective and from the point of view of quantum photonic devices. However, understanding the applications of…

Mesoscale and Nanoscale Physics · Physics 2019-01-23 Jincheng Lu , Rongqian Wang , Jie Ren , Manas Kulkarni , Jian-Hua Jiang

Non-equilibrium phase transitions are studied theoretically for the two-dimensional Hubbard model subject to bias voltages from the electrodes coupled to the system. By combining the fluctuation exchange approximation with the Keldysh…

Strongly Correlated Electrons · Physics 2015-05-20 Takashi Oka , Hideo Aoki

A correct general formula for the spin current through an interacting quantum dot coupled to ferromagnetic leads with magnetization at an arbitrary angle $\theta$ is derived within the framework of the Keldysh formalism. Under asymmetric…

Mesoscale and Nanoscale Physics · Physics 2009-03-18 Hao Zhang , Guang-Ming Zhang , Lu Yu

The functional renormalization group (FRG) approach for spin models relying on a pseudo-fermionic description has proven to be a powerful technique in simulating ground state properties of strongly frustrated magnetic lattices. A drawback…

Strongly Correlated Electrons · Physics 2025-12-17 Janik Potten , Yasir Iqbal , Ronny Thomale , Tobias Müller

We study the electronic current through a quantum dot coupled to two superconducting leads which is driven by either a voltage $V$ or temperature $\Delta T$ bias. Finite biases beyond the linear response regime are considered. The local…

Strongly Correlated Electrons · Physics 2014-06-12 Jan F. Rentrop , Severin G. Jakobs , Volker Meden

Functional methods are used to study magnetoimpurity states of electrons in nanostructures. The Keldysh formalism is applied to these states. The theory is illustrated using a quantum wire sample with impurity atoms capable of localizing…

Mesoscale and Nanoscale Physics · Physics 2008-10-08 A. M. Ermolaev , G. I. Rashba

The theory of quantum transport through a dot under a finite bias voltage is developed using perturbation theory in the Keldysh formalism. It is found that the Kondo resonance splits into double peaks when the voltage exceeds the Kondo…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 Tatsuya Fujii , Kazuo Ueda

We develop a semiclassical theory for spin-dependent quantum transport in ballistic quantum dots. The theory is based on the semiclassical Landauer formula, that we generalize to include spin-orbit and Zeeman interaction. Within this…

Mesoscale and Nanoscale Physics · Physics 2015-06-25 Oleg Zaitsev , Diego Frustaglia , Klaus Richter

Correlation effects within the GW approximation have been incorporated into the Keldysh non-equilibrium transport formalism. We show that GW describes the Kondo effect and the zero-temperature transport properties of the Anderson model…

Materials Science · Physics 2015-06-25 Kristian S. Thygesen , Angel Rubio

In this paper we first derive a Coulomb Hamiltonian for electron--electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix.…

Mathematical Physics · Physics 2014-02-13 Brigitte Bidégaray-Fesquet , Kole Keita

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin…

Strongly Correlated Electrons · Physics 2013-04-11 Andrea Secchi , Sergei Brener , Alexander I. Lichtenstein , Mikhail I. Katsnelson

On the basis of the Keldysh method of non-equilibrium systems, we develop a theory of electron tunneling in normal-metal/superconductor junctions. By using the tunneling Hamiltonian model (being appropriate for the tight-binding systems),…

Superconductivity · Physics 2009-10-31 Xin-Zhong Yan , Hongwei Zhao , Chia-Ren Hu

The thermodynamic properties of ferromagnetic spin chains have been analyzed with a variety of microscopic methods over the years: Bethe ansatz, spin-wave theory, Schwinger-boson mean-field theory, Green functions and renormalization group…

Strongly Correlated Electrons · Physics 2013-05-29 Christoph P. Hofmann

We study non-equilibrium transport through a single-orbital Anderson model in a magnetic field with spin-dependent hopping amplitudes. In the cotunneling regime it is described by an effective spin-1/2 dot with a…

Strongly Correlated Electrons · Physics 2013-01-14 Mikhail Pletyukhov , Dirk Schuricht

We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys.\ Rev.\ B {\bf 64}, 153305 (2001)] to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the…

Mesoscale and Nanoscale Physics · Physics 2020-07-24 Akira Oguri , A. C. Hewson

We develop a non-equilibrium quantum field theory of the free-electron laser based on the Preparata model, using the real-time Keldysh formalism. Starting from a microscopic Lagrangian for a relativistic electron beam coupled to a single…

Quantum Physics · Physics 2025-12-08 Loris Di Cairano

We study the low-temperature thermodynamics of a spin-S magnetic impurity coupled to m degenerate bands of interacting electrons in one dimension. By exploiting boundary conformal field theory techniques, we derive exact results for the…

Strongly Correlated Electrons · Physics 2009-10-30 M. Granath , H. Johannesson