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Register a new userTime-dependent resonant tunneling transport: Keldysh and Kadanoff-Baym nonequilibrium Greens functions in an analytically soluble problem
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Here we address two nonequilibrium Greens functions approaches for a resonant tunneling structure under a sudden switch of a bias. Our aim is to stress that the time-dependent Keldysh formulation of Jauho, Wingreen and Meir, and the partition-free scheme of Stefanucci and Almbladh are formally equivalent in the ubiquitous case of wide-band limit and noninteracting electrons, if leads and dot are in equilibrium before the time-dependent perturbation. We develop explicit closed formulas of the lesser Greens function and time-dependent current, reminding that the different integration limits preclude a face-to-face comparison of two approaches. This study sheds light on both practices, which are of great interest to the mesoscopic transport community.
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Linear response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions with conserving self-energy insertions, thereby satisfying the energy-sum rule. Nucleons are regarded as moving in a mean field defined by an effective mass. A two-body effective (or residual) interaction, represented by a gaussian local interaction, is used to find the effect of correlations in a second order as well as a ring approximation. The response function S(e,q) is calculated for 0.2<q<1.2 fm^{-1}. Comparison is made with the nucleons being un-correlated, RPA+HF only.
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while $2^{nd}$ order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian it local rm potential. We present numerical results for the response function $S(omega,q_0)$ for $q_0=0.2,0.4$ and $0.8 {rm fm}^{-1}$. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the HF+RPA approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sjoberg and followers using methods developped by Babu and Brown, with special emphasis on the induced interaction.
This review provides a written version of the lectures presented at the Schladming Winter School 2008, Austria, on Nonequilibrium Aspects of Quantum Field Theory. In particular, it shows the way from quantum-field theory - in two-particle irreducible approximation - to the Kadanoff-Baym (KB) equations and various approximations schemes of the KB equations in phase space. This ultimately leads to the formulation of an off-shell transport theory that well incorporates the underlying quantum physics. Remarkably, these transport equations may be solved within a testparticle representation that allows to study non-equilibrium quantum systems in the weak and strong coupling regime. Actual applications to dilepton production in heavy-ion reactions are presented in comparison with available data. The approach, furthermore, allows to address the hadronization process from partonic to hadronic degrees of freedom.
To calculate the baryon asymmetry in the baryogenesis via leptogenesis scenario one usually uses Boltzmann equations with transition amplitudes computed in vacuum. However, the hot and dense medium and, potentially, the expansion of the universe can affect the collision terms and hence the generated asymmetry. In this paper we derive the Boltzmann equation in the curved space-time from (first-principle) Kadanoff-Baym equations. As one expects from general considerations, the derived equations are covariant generalizations of the corresponding equations in Minkowski space-time. We find that, after the necessary approximations have been performed, only the left-hand side of the Boltzmann equation depends on the space-time metric. The amplitudes in the collision term on the right--hand side are independent of the metric, which justifies earlier calculations where this has been assumed implicitly. At tree level, the matrix elements coincide with those computed in vacuum. However, the loop contributions involve additional integrals over the the distribution function.
The early stage density oscillations of the electronic charge in molecules irradiated by an attosecond XUV pulse takes place on femto- or subfemtosecond timescales. This ultrafast charge migration process is a central topic in attoscience as it dictates the relaxation pathways of the molecular structure. A predictive quantum theory of ultrafast charge migration should incorporate the atomistic details of the molecule, electronic correlations and the multitude of ionization channels activated by the broad-bandwidth XUV pulse. In this work we propose a first-principles Non Equilibrium Greens Function method fulfilling all three requirements, and apply it to a recent experiment on the photoexcited phenylalanine aminoacid. Our results show that dynamical correlations are necessary for a quantitative overall agreement with the experimental data. In particular, we are able to capture the transient oscillations at frequencies 0.15PHz and 0.30PHz in the hole density of the amine group, as well as their suppression and the concomitant development of a new oscillation at frequency 0.25PHz after about 14 femtoseconds.
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