In a recent Letter, Schöne and Eguiluz (SE) [1] present a self-consistent calculation of self-energy in GW and polarization in the GG approximation. The main progress in [1] is to use full Green's functions (GF's) including damping and renormalization of the oneparticle states instead of a simple quasiparticle picture. However, SE find the calculated band gap energies to disagree with experimental results. SE suggested the GW approximation to be not appropriate. From our point of view, the reason is less the GW approximation, but more the construction of a corresponding polarization function.The question of self-consistent approximations for self-energy and polarization was discussed by Baym and Kadanoff [2,3]. They stated that the mean field (Hartree) description is consistent with an RPA polarization function. Since the Hartree field vanishes because of electroneutrality, free GF's should be used in this approximation. This is the reason why other authors used a so-called restricted self-consistent approach with a fixed polarization function [2]. More general, Ward's identity [5] connects any frequency dependent damping with vertex corrections. This identity is related to gauge invariance ensuring charge conservation [6] and leads to the f-sum rule for the inverse dielectric function [7], given byIt is not our aim to discuss systematically which polarization function is related with the GW approximation for the self-energy [8,9], but we show that at least the first vertex correction in the polarization function, given in Keldysh notation byhas to be taken into account. A self-consistent, iterative calculation of self-energy and polarization (in the GG approximation) was already presented [10]. Here, we include the vertex correction P 0 , calculated with free GF's and a dynamically screened interaction. Figure 1 shows the f sum for an electron gas with T 0.6 Ry and n e 1.5 3 10 25 a 23 B . Main contributions to the self-energy come from small q values; q ϳ0 5k D (k D : inverse Debye radius), where a plasmon exists. In this region, an RPA polarization function with dressed GF's leads to a strong violation of the f-sum rule. From our point of view, this (and not the GW approximation for the selfenergy) seems to be the main reason why the results in [1] fail to agree with experimental data.Another method to construct conserving approximations, which is based on a linear response approach, is 5 10 15 20 1 2 3 4 5 6 7 8 9 q [κ ] D exact self-cons. RPA self-cons. RPA + Vertex FIG. 1. f-sum rule as a function of q.given in [11]. It allows one to include collisions in the polarization function in such a way that the sum rules are fulfilled within the numerical accuracy. The determination of the polarization function from kinetic theory [12] also allows one to fulfill the f-sum rule within numerical accuracy [13].

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Electronic transitions in biaxial F-ZnPz are studied by two-photon absorption. The anisotropy of the crystal leads to a large energy splitting of the P excitons. The energy shift of the P excitons and Landau transitions axe observed in a magnetic field up to 6T. We present a theory which describes the anisotropic P excitons in a magnetic field. The analysis of the experimental data allows the determination of the anisotropic dielectric constants and effective masses of the valence and conduction bands.

In this paper we discuss pulsed laser excitation, which is nearly resonant with an atomic transition in a partially ionized plasma. The dynamics of particles and the external laser field is microscopically described by a Green's function approach on the one-and tw-particle level. Particularly for the (1s + 2p) transition of hydrogen the influence of the particle density, laser intensity and detuning on the polarization dynamics is discussed. Treating the collision integral with the Lipavsky ansatz allows to determine the relaxation times TI and Tz for the inversion and the polarization. These relaxation times vary from the p3 scale (in the low-density case) to the f3 region (at high densities). Considering the pulse duration in comparison with the relaxation times, the Markovian limit is valid for moderate and high densities, whereas the low-density caSe requires a non-Markovian computation.

In low-dimensional systems, quantum-confinement and bandstructure effects strongly influence the many-particle effects that ultimately give rise to the nonlinear optical properties of semiconductores. In this paper, we use a Keldysh Greens functions approach to obtain numerical results for isolated quantum wells and coupled superlattices, and investigate in different limits the combination of band-structure and many-particle effects. The inclusion of higher order Coulomb correlations gives rise to deviations from the results found in the literature for low carrier densities and temperatures, which increase with the fundamental band gap, and may be relevant for future optical device design and operation. The optical spectra presented illustrate the theoretical approach and provide insight on the physical mechanisms responsible for lasing in wide-band gap heterostructures, as contrasted to the usual 111-V systems.