Table of contents

(The PDF contains: an obituary and in memoriam for David C. Langreth, a list of the conference participants, a complete list of the conference talks and posters and several photographs taken during the conference. )

The fifth interdisciplinary conference 'Progress in Nonequilibrium Green's Functions' (PNGF5) was held at the University of Jyväskylä, Finland, on 27--31 August 2012. The conference continued the successful tradition of its predecessors (Rostock 1999, Dresden 2002, Kiel 2005 and Glasgow 2009) to bring together different communities for an interdisciplinary exchange of recent results and theoretical concepts.

The conference focused on recent developments, current challenges and future perspectives in nonequilibrium Green's functions theory in various fields of physics but included also other many-body methods. Roughly 20 invited talks were given by some of the top scientists in the field, accompanied by 10 contributed talks. (Slides of several presentations can be found online at www.jyu.fi/physics/pngf5.) Also a poster session was set up to enhance scientific discussions, building up new collaborations and enriching views and ideas. As at the previous meetings, the atmosphere was interactive and stimulating, benefitting both experienced scientists and young researchers and students.

The present volume contains 14 articles based on works presented at this conference. The articles partly have review character so they should be of use for an interdisciplinary community working or interested in nonequilibrium Green's functions. All papers were refereed according to high scientific standards.

The conference would not have been possible without financial support from the Federation of Finnish Learned Societies, Finnish Academy of Science and Letters and Nanoscience Center of the university of Jyväskylä which are greatly acknowledged. The local organizing committee is also grateful to the administration personnel, Marjut Hilska and Riitta-Liisa Kuittinen, for assistance. We further thank professor Antti-Pekka Jauho for invaluable help and advice during the organization of the conference.

The editors of the present conference proceedings acknowledge the authors for their excellent papers and all the referees for participating in a thorough peer-reviewing of the manuscripts. Finally, it is our pleasure to announce that the sixth conference 'Progress in Nonequilibrium Green's Functions' (PNGF6) will be held in August 2015 at the University of Lund, Sweden.

Riku Tuovinen and Robert van Leeuwen University of Jyväskylä Michael Bonitz University of Kiel February 2013

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel'. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick's theorem that is at the same time valid in all these flavors of many-body theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green's function with appropriate boundary conditions. We further discuss a generalized Wick theorem for general initial states on the Keldysh contour and derive how the formalisms based on the Keldysh and Konstantinov-Perel'-contours are related for the case of general initial states.

The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green functions—the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane—for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.

The carrier dynamics in bulk Silicon, a paradigmatic indirect gap semiconductor, is studied by using the Baym–Kadanoff equations. Both the electron–electron (e–e) and electron–phonon (e–p) self-energies are calculated fully ab–initio by using a semi–static out–of– equilibrium GW approximation in the e–e case and a Fan self–energy in the e-p case. By using the generalized Baym–Kadanoff ansatz the two–time evolution is replaced by the only dynamics on the macroscopic time axis. The enormous numerical difficulties connected with a real–time simulation of realistic systems is overcome by using a completed collision approximation that further simplifies the memory effects connected to the time evolution. The carrier dynamics is shown to reduce in such a way to have stringent connections to the well–known equilibrium electron–electron and electron–phonon self–energies. This link allows to use general arguments to motivate the relative balance between the e–e and e–p scattering channels on the basis of the carrier energies.

A theory of scattering processes between the electronic configurations of a single quantum dot (QD) in interaction with LO phonons is presented. Polaronic renormalizations of the QD carriers are taken into account using a Green's function approach and play an essential role in the calculation of the scattering rates. Moreover, the rates are configuration-dependent, so that additional carriers in the QD, that do not take part in a transition, influence its efficiency. The QD carrier correlations are fully included by using a von Neumann-Lindblad formalism in the configuration basis. Numerical results for scattering rates and QD carrier dynamics are shown to illustrate the theory.

Using dynamical mean-field theory and the non-crossing approximation as impurity solver, we study the response of a Mott insulator to strong dc electric fields. The breakdown of the Mott insulating state is triggered by field-induced creation of doublon-hole pairs. In a previous investigation, Ref. [1], it was found that the system approaches a long-lived quasi-steady state in which the current is time-independent although the number of carriers constantly increases. Here we investigate and clarify the nature of this state, which exists only because thermalization is slow in the Hubbard model at strong coupling. The current is time-independent because doublons and holes have an infinite temperature distribution. Evidence for this fact is obtained from spectral functions and by comparing the electric current with the field-induced doublon-hole creation rate. Implications to real experiments, in systems with energy dissipation, are discussed.

For a minimal Hubbard-type system at different interaction strengths U, we investigate the density-response for an excitation beyond the linear regime using the generalized Kadanoff-Baym ansatz (GKBA) and the second Born (2B) approximation. We find strong correlation features in the response spectra and establish the connection to an involved double excitation process. By comparing approximate and exact Green's function results, we also observe an anomalous U-dependence of the energy of this double excitation in 2B+GKBA. This is in accordance with earlier findings [K. Balzer et al., EPL 98, 67002 (2012)] on double excitations in quantum wells.

We give a presentation on the time-dependent restricted active space Configuration Interaction method, which has been recently introduced [D. Hochstuhl, M. Bonitz, PRA, in press] to efficiently tackle the few-particle nonequilibrium many-body problem. Particularly, we apply it to the calculation of photoionization cross sections and angular resolved ionization yields of groundstate neon.

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 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 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.

Here we analyze this correspondence by studying the generalized Kadanoff–Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

Transport coefficients provide a unique insight into the near-equilibrium behavior of quantum many-body systems. The mean-free path, λ, of a particle within a dense medium is a basic transport coefficient, at the basis of several theoretical concepts and closely related to experimentally measured quantities. Green's functions techniques are particularly well suited to study such transport properties, since they are naturally formulated in the time domain. We present a calculation of the mean-free path of a nucleon in symmetric nuclear matter using self-consistent ladder self-energies extended to the complex energy plane. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 femtometers.

Semiclassical time-dependent approaches are nowadays able to describe energetic central collisions of heavy isotopes with minimal assumptions. Simulations in the mean-field picture have provided insight on both nuclear structure and low-energy many-body reaction mechanisms. In this context, nonequilibrium Greens functions techniques have the potential to improve the description of the time evolution of nuclear systems by introducing effects beyond the mean-field. We describe a first attempt to use the Kadanoff-Baym dynamics for one-dimensional nuclear systems, with a particular emphasis on the process of correlation buildup.

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions We consider a model single-molecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of the electron density matrix, one interaction is diagonal in the central region and the second off-diagonal between the central region and the left electrode. We use a non-equilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and within a dynamical mean-field-like approach for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasi-resonant regime, and for a wide range of parameters. They show that a non-equilibrium (i.e. bias dependent) dynamical (i.e. energy dependent) renormalisation is obtained for the contact between the left electrode and the central region in the form of a non-equilibrium renormalisation of the lead embedding potential. The conductance is affected by the renormalisation of the contact: the amplitude of the main resonance peak is modified as well as 'the lineshape of the first vibron side-band.

We review a recent theoretical development based on non-equilibrium Green's function formalism to study heat transport in nanomechanical devices modeled by phononic systems of coupled quantum oscillators driven by ac forces and connected to phononic reservoirs. We present the relevant equations to calculate the heat currents flowing along different regions of the setup, as well as the power developed by the time-dependent forces. We also present different strategies to evaluate the Green's functions exactly or approximately within the weak driving regime. We finally discuss the different mechanisms in which the ac driving forces deliver the energy. We show that, besides generating heat, the forces may operate exchanging energy as a quantum engine.

Recently the interest in quantum interference (QI) phenomena in molecular devices (molecular junctions) has been growing due to the unique features observed in the transmission spectra. In order to design single molecular devices exploiting QI effects as desired, it is necessary to provide simple rules for predicting the appearance of QI effects such as anti-resonances or Fano line shapes and for controlling them. In this study, we derive a transmission function of a generic molecular junction with a side group (T-shaped molecular junction) using a minimal toy model. We developed a simple method to predict the appearance of quantum interference, Fano resonances or anti- resonances, and its position in the conductance spectrum by introducing a simple graphical representation (parabolic model). Using it we can easily visualize the relation between the key electronic parameters and the positions of normal resonant peaks and anti-resonant peaks induced by quantum interference in the conductance spectrum. We also demonstrate Fano and anti-resonance in T-shaped molecular junctions using a simple tight-binding model. This parabolic model enables one to infer on-site energies of T-shaped molecules and the coupling between side group and main conduction channel from transmission spectra.

We solve analytically the Kadanoff–Baym equations for a noninteracting junction connected to an arbitrary number of noninteracting wide-band terminals. The initial equilibrium state is properly described by the addition of an imaginary track to the time contour. From the solution we obtain the time-dependent electron densities and currents within the junction. The final results are analytic expressions as a function of time, and therefore no time propagation is needed – either in transient or in steady-state regimes. We further present and discuss some applications of the obtained formulae.