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The Journal of Chemical Physics

Generalized Equation of Motion for a Gas Using the Quantum-Mechanical Green's Function Technique. I

R. Paul, G.N. Fowler

Published Jan 1, 1968• 12 citations
Publisher

Abstract

The quantum-mechanical Green's function technique of Kadanoff and Baym is extended to include non-Markowian effects in order to make contact with the results of Prigogine.
DOI
10.1063/1.1667990

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The generalized Kadanoff-Baym ansatz (GKBA) is an approximation to the Kadanoff-Baym equations (KBE), that neglects certain memory effects that contribute to the Green's function at non-equal times. Here we present arguments and numerical results to demonstrate the practical insignificance of the quantities neglected when deriving the GKBA at conditions at which KBE and GKBA are appropriate. We provide a mathematical proof that places a scaling bound on the neglected terms, further reinforcing that these terms are typically small in comparison to terms that are kept in the GKBA. We perform calculations in a range of models, including different system sizes and filling fractions, as well as experimentally relevant non-equilibrium excitations. We find that both the GKBA and KBE capture the dynamics of interacting systems with moderate and even strong interactions well. We explicitly compute terms neglected in the GKBA approximation and show, in the scenarios tested here, that they are orders of magnitude smaller than the terms that are accounted for, i.e., they offer only a small correction when included in the full Kadanoff-Baym equations.
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