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Spectral Properties

Klaus Morawetz

Published Dec 21, 2017• 0 citations
Publisher

Abstract

Abstract The spectral properties of the nonequilibrium Green’s functions are explored. Causality and sum rules are shown to be completed by the extended quasiparticle picture. The off-shell motion is seen to become visible in satellite structures of the spectral function. Different forms of ansatz to reduce the two-time Green’s function to a one-time reduced density matrix are discussed with respect to the consistency to other approximations. We have seen from the information contained in the correlation function that the statistical weight of excitations with which the distributions are populated are given by the spectral function. This momentum-resolved density of state can be found by the retarded and advance functions.

DOI
10.1093/oso/9780198797241.003.0008

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Abstract The gradient approximations of the Kadanoff and Baym equations are derived up to first order. The off-shell motions responsible for the satellites are shown to ensure causality. The cancellation of off-shell motions from the drift and correlation part of the reduced density provides a precursor of the kinetic equation for the quasiparticle distribution which leads to a functional between reduced and quasiparticle distribution, named the extended quasiparticle picture. Virial corrections appear as internal gradients in the selfenergy and therefore in the considered processes. With this extended quasiparticle picture, the non-Markovian kinetic equations are transformed into Markovian ones for proper defined quasiparticles without neglect showing the exact cancellation of off-shell parts. Alternative approaches are discussed for comparison.
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