Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.Comment: 16 pages, 9 figures. Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc

Image charge dynamics in time-dependent quantum transport

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 figure

Generalized Master equation approach to mesoscopic time-dependent transport

We use a generalized Master equation (GME) formalism to describe the non-equilibrium time-dependent transport through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire are modulated by out-of-phase time-dependent functions which simulate a turnstile device. One lead is fixed at one end of the sample whereas the other lead has a variable placement. The system is described by a lattice model. We find that the currents in both leads depend on the placement of the second lead. In the rather small bias regime we obtain transient currents flowing against the bias for short time intervals. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method

Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects

We study time-dependent quantum transport in a correlated model system by means of time-propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green function. We consider an initially contacted equilibrium system of a correlated central region coupled to tight-binding leads. Subsequently a time-dependent bias is switched on after which we follow in detail the time-evolution of the system. Important features of the Kadanoff-Baym approach are 1) the possibility of studying the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We find that initial correlation and memory terms due to many-body interactions have a large effect on the transient currents. Furthermore the value of the steady state current is found to be strongly dependent on the approximation used to treat the electronic interactions.Comment: 5 pages, 2 figure

Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems

Two-particle irreducible effective action approach to nonlinear current conserving approximations in driven systems

Using closed-time path two-particle irreducible coarse-grained effective action (CTP 2PI CGEA) techniques, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the CTP 2PI CGEA is invariant under a simultaneous gauge transformation of the external field and the full Schwinger-Keldysh propagator, and that this property holds even when the loop expansion of the CTP 2PI CGEA is truncated at arbitrary order. The effective action approach provides a systematic way of calculating the propagator and response functions of the system, via the Schwinger-Dyson equation and the Bethe-Salpeter equations, respectively. We show that, due to the invariance of the CTP 2PI CGEA under external gauge transformations, the response functions calculated from it satisfy the Ward-Takahashi hierarchy, thus warranting the conservation of the electronic current beyond the expectation value level. We also clarify the connection between nonlinear response theory and the WT hierarchy, and discuss an example of an ad hoc approximation that violate it. These findings may be useful in the study of current fluctuations in correlated electronic pumping devices.Comment: 30 pages. Accepted for publication in JPC

Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models

In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allows for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies. As atomic and molecular examples we consider the He atom and the linear version of H$_3^+$ in one spatial dimension. For these closed-shell models we, in Hartree-Fock and second Born approximation, compute the ground-state properties and compare with the exact findings obtained from the solution of the few-particle time-dependent Schr\"odinger equation.Comment: 12 pages, 3 figures, submitted as proceedings of conference "PNGF IV

Tetrazole as a Replacement of the Electrophilic Group in Characteristic Prolyl Oligopeptidase Inhibitors

4-Phenylbutanoyl-aminoacyl-2(S)-tetrazolylpyrrolidines were studied as prolyl oligopeptidase inhibitors. The compounds were more potent than expected from the assumption that the tetrazole would also here be a bioisostere of the carboxylic acid group and the corresponding carboxylic acids are at their best only weak inhibitors. The aminoacyl groups L-prolyl and L-alanyl gave potent inhibitors with IC50 values of 12 and 129 nM, respectively. This was in line with typical prolyl oligopeptidase inhibitors; however, we did observe a difference with N-methyl-L-alanyl, which gave potent inhibitors in typical prolyl oligopeptidase inhibitors but not in our novel compound series. Furthermore, all studied 4-phenylbutanoyl-aminoacyl-2(S)-tetrazolylpyrrolidines decreased alpha-synuclein dimerization at the concentration of 10 mu M, also when they were only weak inhibitors of the proteolytic activity of the enzyme with an IC50 value of 205 mu M. Molecular docking studies revealed that the compounds are likely to bind differently to the enzyme compared to typical prolyl oligopeptidase inhibitors represented in this study by 4-phenylbutanoyl-aminoacyl-2(S)-cyanopyrrolidines.Peer reviewe

Removal of proteinase K resistant alpha Syn species does not correlate with cell survival in a virus vector-based Parkinson's disease mouse model

Parkinson's disease (PD) is characterized by degeneration of nigrostriatal dopaminergic neurons and accumu-lation of alpha-synuclein (alpha Syn) as Lewy bodies. Currently, there is no disease-modifying therapy available for PD. We have shown that a small molecular inhibitor for prolyl oligopeptidase (PREP), KYP-2047, relieves alpha Syn-induced toxicity in various PD models by inducing autophagy and preventing alpha Syn aggregation. In this study, we wanted to study the effects of PREP inhibition on different alpha Syn species by using cell culture and in vivo models.We used Neuro2A cells with transient alpha Syn overexpression and oxidative stress or proteasomal inhibition -induced alpha Syn aggregation to assess the effect of KYP-2047 on soluble alpha Syn oligomers and on cell viability. Here, the levels of soluble alpha Syn were measured by using ELISA, and the impact of KYP-2047 was compared to anle138b, nilotinib and deferiprone. To evaluate the effect of KYP-2047 on alpha Syn fibrillization in vivo, we used unilateral nigral AAV1/2-A53T-alpha Syn mouse model, where the KYP-2047 treatment was initiated two-or four -weeks post injection.KYP-2047 and anle138b protected cells from alpha Syn toxicity but interestingly, KYP-2047 did not reduce soluble alpha Syn oligomers. In AAV-A53T-alpha Syn mouse model, KYP-2047 reduced significantly proteinase K-resistant alpha Syn oligomers and oxidative damage related to alpha Syn aggregation. However, the KYP-2047 treatment that was initiated at the time of symptom onset, failed to protect the nigrostriatal dopaminergic neurons. Our results emphasize the importance of whole alpha Syn aggregation process in the pathology of PD and raise an important question about the forms of alpha Syn that are reasonable targets for PD drug therapy.Peer reviewe

Kadanoff-Baym approach to double-excitations in finite systems

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 figure