Search

Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\Sigma$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the $GW$ approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction $W$) self-energy diagrams lead to improved electron spectral functions (SF) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral function. The resolution of this difficulty has been demonstrated in our previous works. The main idea is to represent the self-energy operator in a Fermi Golden rule form which leads to the manifestly positive definite SF and allows for a very efficient numerical algorithm. So far, the method has only been applied to 3D electron gas, which is a paradigmatic system, but a rather simple one. Here, we systematically extend the method to 2D including realistic systems such as mono and bilayer graphene. We focus on one of the most important vertex function effects involving the exchange of two particles in the final state. We demonstrate that it should be evaluated with the proper screening and discuss its influence on the quasiparticle properties.

We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on bulk sodium, appearance of the secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed.

We give details on how to calculate spectral functions and Green's functions for finite systems using the Chebyshev polynomial expansion method. We apply the method to a finite Anderson impurity system, and furthermore give details on how to exploit its symmetry to transform the system into smaller orthogonal subsystems. We also consider systems connected to infinite leads, which we study by approximating the unknown self-energy with an exact self-energy for a finite system. As our test case, we consider the single-impurity Anderson model, where we find that we can capture some aspects of Kondo physics., Comment: 10 pages, 6 figures, Part of Progress in Nonequilibrium Green's Functions VI proceedings

We investigate the effect of mechanical strain on the dynamics of thin $\mathrm{MoS_2}$ nanodrum resonators. Using a piezoelectric crystal, compressive and tensile biaxial strain is induced in initially flat and buckled devices. In the flat device, we observe a remarkable strain-dependence of the resonance line width, while the change in the resonance frequency is relatively small. In the buckled device, the strain-dependence of the damping is less pronounced, and a clear hysteresis is observed. The experiment suggests that geometric imperfections, such as microscopic wrinkles, could play a role in the strong dissipation observed in nanoresonators fabricated from 2-D materials., Comment: 11 pages, 3 figures

We put forward a first-principle NonEquilibrium Green's Function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin samples. The method can deal with pump fields of arbitrary strength, frequency and duration as well as for overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing the pump-probe delay $\t$, and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of {\em dynamical correlation} effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of Kr$^{2+}$ with respect to Kr$^{1+}$ as a function of $\t$., Comment: 13 pages, 8 captioned figures

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state, and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Ref. [arXiv:1403.2968]. We show that choosing a homogeneous ground state solution leads to unstable dynamics for a sufficiently strong interaction, and that allowing a symmetry-broken state prevents this. The instability is caused by the bifurcation of the ground state and understood physically to be connected with the bipolaronic crossover of the exact system. This mean-field instability persists in the partially self-consistent Born approximation but is not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This functions amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid, and how they fail to describe the studied exact properties of the chosen model system., Comment: 12 figures

Nanocrystalline diamond (NCD) is a promising material for electronic and mechanical micro- and nanodevices. Here we introduce a versatile pick-up and drop technique that makes it possible to investigate the electrical, optical and mechanical properties of as-grown NCD films. Using this technique, NCD nanosheets, as thin as 55 nm, can be picked-up from a growth substrate and positioned on another substrate. As a proof of concept, electronic devices and mechanical resonators are fabricated and their properties are characterized. In addition, the versatility of the method is further explored by transferring NCD nanosheets onto an optical fibre, which allows measuring its optical absorption. Finally, we show that NCD nanosheets can also be transferred onto 2D crystals, such as MoS2, to fabricate heterostructures. Pick-up and drop transfer enables the fabrication of a variety of NCD-based devices without requiring lithography or wet processing., Comment: 15 pages, 6 figures

In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We write the generic diagram for the density-response spectrum as the sum of partitions. In a partition the original diagram is evaluated using time-ordered Green's functions (GF) on the left-half of the diagram, antitime-ordered GF on the right-half of the diagram and lesser or greater GF gluing the two halves. As there exist more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare GF and subsequently extend it to dressed GF. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zero-th order bubble diagram, the first-order vertex diagram and a partition of the second-order ladder diagram. We evaluate this approximation in the 3D homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities., Comment: 19 pages, 19 figures

Today graphene nanoribbons and other graphene-based nanostructures can be synthesized with atomic precision. But while investigations have concentrated on straight graphene ribbons of fixed crystal orientation, ribbons with intrinsic curvature have remained mainly unexplored. Here, we investigate electronic transport in intrinsically curved graphene nanoribbons coupled to straight leads, using two computational approaches. Stationary approach shows that while the straight leads govern the conductance gap, the presence of curvature blurs the gap and reduces on-off ratio. An advanced time-dependent approach shows that behind the fa\c{c}ade of calm stationary transport the currents run violently: curvature triggers temporally and spatially focused electric currents, to the extent that for short durations single carbon-carbon bonds carry currents far exceeding the steady-state currents in the entire ribbons. Recognizing this focusing is pivotal for a robust design of graphene sensors and circuitries.

In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this method can also be used to perform flexible and efficient quantum control. The simple interpretation of the density (the amount of electrons per volume) allows us to use our physical intuition to consider interesting control problems and to easily restrict the search space in optimization problems. The method's origin in time-dependent density-functional theory makes studies of large systems possible. We further discuss the generalization of the method to higher dimensions and its numerical implementation in great detail. We also present several examples to illustrate the flexibility, and to confirm that the scheme is efficient and stable even for large and rapid density variations irrespective of the initial state and interactions.

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte-Carlo momentum integrations to evaluate the diagrams., Comment: 19 pages, 19 figures

We measure the energy relaxation rate of single- and few-layer molybdenum disulphide ($\mathrm{MoS_2}$) nanomechanical resonators by detecting the resonator ring-down. Recent experiments on these devices show a remarkably low quality (Q)-factor when taking spectrum measurements at room temperature. The origin of the low spectral Q-factor is an open question, and it has been proposed that besides dissipative processes, frequency fluctuations contribute significantly to the resonance line-width. The spectral measurements performed thus far however, do not allow one to distinguish these two processes. Here, we use time-domain measurements to quantify the dissipation. We compare the Q-factor obtained from the ring-down measurements to those obtained from the thermal noise spectrum and from the frequency response of the driven device. In few-layer and single-layer $\mathrm{MoS_2}$ resonators the two are in close agreement, which demonstrates that the spectral line-width in $\mathrm{MoS_2}$ membranes at room temperature is limited by dissipation, and that excess spectral broadening plays a negligible role., Comment: 13 pages, 5 figures

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong whereas at smaller interactions only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction., Comment: 9 figures, corrected typos

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions and near degeneracy static correlations. In this work we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function $f(r_{12})$ depending on the interelectronic distance $r_{12}$. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function Ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function $f(r_{12})$ needs to diverge for large $r_{12}$ at large internuclear distances while for shorter bond distances it increases as a function of $r_{12}$ to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior., Comment: 16 pages, 13 figures

We derive an exact expression for the photo-current of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photo-current within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photo-current is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector., Comment: 11 pages, 11 figures

Real-time Green's function simulations of molecular junctions (open quantum systems) are typically performed by solving the Kadanoff-Baym equations (KBE). The KBE, however, impose a serious limitation on the maximum propagation time due to the large memory storage needed. In this work we propose a simplified Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA) to overcome the KBE limitation on time, significantly speed up the calculations, and yet stay close to the KBE results. This is achieved through a twofold advance: first we show how to make the GKBA work in open systems and then construct a suitable quasi-particle propagator that includes correlation effects in a diagrammatic fashion. We also provide evidence that our GKBA scheme, although already in good agreement with the KBE approach, can be further improved without increasing the computational cost., Comment: 13 pages, 13 figures

The non-vanishing of the natural orbital occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' Theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wave function leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wave-functions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of two-particle systems that in case the wave function is non-analytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are non-vanishing. We further derive a more general criterium for the non-vanishing of NO occupations for two-particle wave functions with a certain separability structure. On the basis of this criterium we show that for a two-particle system of harmonically confined electrons with a Coulombic interaction (the so-called Hookium) the natural orbital occupations never vanish., Comment: 15 pages, 2 figures

We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting particles in a singlet state. In this case the initial state is completely determined by the initial density, the initial time-derivative of the density and a single integer that characterizes the (angular) momentum of the system. We then give an exact analytic expression for the exchange-correlation potential that relates two non-interacting systems with different initial states. This is used to demonstrate how the Kohn-Sham procedure predicts the density of a reference system without the need of solving the reference system's Schr\"odinger equation. We further numerically construct the exchange-correlation potential for an analytically solvable system of two electrons on a quantum ring with a squared cosine two-body interaction. For the same case we derive an explicit analytic expression for the exchange-correlation kernel and analyze its frequency-dependence (memory) in detail. We compare the result to simple adiabatic approximations and investigate the single-pole approximation. These approximations fail to describe the doubly-excited states, but perform well in describing the singly-excited states., Comment: 12 pages, 5 figures

We present a local control scheme to construct the external potential v that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. The numerical method is efficient and stable even for large and rapid density variations irrespective of the initial state and the interactions. The method can at the same time be used to answer fundamental v-representability questions in density-functional theory. In particular, in the absence of interactions, it allows us to construct the exact time-dependent Kohn-Sham potential for arbitrary initial states. We illustrate the method in a correlated one-dimensional two-electron system with different interactions, initial states and densities. For a Kohn-Sham system with a correlated initial state we demonstrate the interplay between memory and initial-state dependence as well as the failure of any adiabatic approximation., Comment: 5 pages, 3 figures

We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of $\mathrm{0.8\,Hz}$ is observed for a mode with a line width of $\mathrm{5.8\,Hz}$ in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of $\mathrm{4.5\times10^5}$ for our top-down fabricated micromechanical beam resonators., Comment: 9 pages, 2 figures

In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an explicit relation between the boundary conditions on the density and the convergence properties of the fixed-point procedure via the spectral properties of the associated Sturm-Liouville operator. We show precisely under which conditions discrete and continuous spectra arise and give explicit examples. These conditions are then used to show that in the most physically relevant cases the fixed point procedure converges. This is further demonstrated with an example., Comment: 20 pages, 8 figures, 3 tables

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability., Comment: 13 pages, 12 figures

We derive the semiclassical Kirzhnits expansion of the D-dimensional one-particle density matrix up to the second order in $\hbar$. We focus on the two-dimensional (2D) case and show that all the gradient corrections both to the 2D one-particle density and to the kinetic energy density vanish. However, the 2D Kirzhnits expansion satisfies the consistency criterion of Gross and Proetto [J. Chem. Theory Comput. 5, 844 (2009)] for the functional derivatives of the density and the noninteracting kinetic energy with respect to the Kohn-Sham potential. Finally we show that the gradient correction to the exchange energy diverges in agreement with the previous linear-response study.

In this work we investigate the effects of the electron-electron interaction between a molecular junction and the metallic leads in time-dependent quantum transport. We employ the recently developed embedded Kadanoff-Baym method [Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction changes substantially the transient and steady-state transport properties. We first show that the mean-field Hartree-Fock (HF) approximation does not capture the polarization effects responsible for the renormalization of the molecular levels neither in nor out of equilibrium. Furthermore, due to the time-local nature of the HF self-energy there exists a region in parameter space for which the system does not relax after the switch-on of a bias voltage. These and other artifacts of the HF approximation disappear when including correlations at the second-Born or GW levels. Both these approximations contain polarization diagrams which correctly account for the screening of the charged molecule. We find that by changing the molecule-lead interaction the ratio between the screening and relaxation time changes, an effect which must be properly taken into account in any realistic time-dependent simulation. Another important finding is that while in equilibrium the molecule-lead interaction is responsible for a reduction of the HOMO-LUMO gap and for a substantial redistribution of the spectral weight between the main spectral peaks and the induced satellite spectrum, in the biased system it can have the opposite effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap., Comment: 18 pages, 26 figures

We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are characterized as double-excitations., Comment: 20 pages, 10 figures

We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the exchange correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities which indicates that the exchange correlation potential must attain nonzero values in the leads., Comment: 11 pages, 9 figures

We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined by real-time propagation of the Kadanoff-Baym equations after applying a bias voltage to the system. The electronic interactions on the central site are incorporated by means of self-energy approximations at Hartree-Fock, second Born and GW level. We investigate the conditions under which multiple steady-state solutions occur within different self-energy approximations, and analyze in detail the nature of these states from an analysis of their spectral functions. At the Hartree-Fock level at least two stable steady-state solutions with different densities and currents can be found. By applying a gate voltage-pulse at a given time we are able to switch between these solutions. With the same parameters we find only one steady-state solution when the self-consistent second Born and GW approximations are considered. We therefore conclude that treatment of many-body interactions beyond mean-field can destroy bistability and lead to qualitatively different results as compared those at mean-field level., Comment: 10 pages, 8 figures, Submitted at "Progress in Nonequilibrium Green's Functions IV" conference

We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties., Comment: 9 pages, 5 figure; extended version published in Phys. Rev. B

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for the zero and finite temperature charge carrier density, the orbital-resolved distribution functions and the self-consistent total energies and spectral functions for isotropic, two-dimensional parabolic confinement as well as for the limit of large anisotropy--quasi-one-dimensional entrapment. For the considered quantum dots with N=2, 3 and 6 electrons, the analysis comprises the crossover from Fermi gas/liquid (at large carrier density) to Wigner molecule or crystal behavior (in the low-density limit).

It is proven that the center of mass (COM or Kohn) oscillation of a many-body system in a harmonic trap coincides with the motion of a single particle as long as conserving approximations are applied to treat the interactions. The two conditions formulated by Kadanoff and Baym \cite{kb-book} are shown to be sufficient to preserve the COM mode. The result equally applies to zero and finite temperature, as well as to nonequilibrium situations, and to the linear and nonlinear response regimes.