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Journal of Mathematical Physics

Time-reversal noninvariance of the quantum-mechanical kinetic equation of Kadanoff and Baym

Zlatiborka A. Nikolić

Published Dec 1, 1978• 0 citations
Publisher

Abstract

Applying anticausal Green’s function technique, it has been shown that the origin of time-reversal noninvariance of the quantum-mechanical kinetic equation of Kadanoff and Baym lies in the selection of the boundary condition that the system be in thermodynamical equilibrium at time t=−∞.
DOI
10.1063/1.523648

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Equilibrium and nonequilibrium properties of nonideal many-particle systems are strongly influenced by correlation effects that are well described by generalized quantum kinetic equations, in particular, the Kadanoff-Baym equations (KBE). However, these equations are usually derived under the assumption of the weakening of initial correlations (Bogolyubov's condition) and, therefore, fail to correctly describe the short time behavior. We demonstrate that this assumption is not necessary for the derivation of the KBE. Using functional derivatives techniques, we present a straightforward generalization of the KBE that allows us to include arbitrary initial correlations and that is more general than previous derivations. As a result, an additional collision integral is obtained, which is being damped out after a few collisions. Our results are complemented with numerical investigations showing the effect of initial correlations.
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Abstract An approximation of the Green function based on the Generalized Kadanoff–Baym Ansatz and its correction is tested on the electron tunneling through a single atom, incorporating the on-site second-order Born interaction. Time evolution resulting from the corresponding kinetic equation for the density matrix is compared with the direct solution of the non-equilibrium Green functions. It is demonstrated that the short-time nature of corrections beyond the Generalized Kadanoff–Baym Ansatz enables their effective numerical approximation. Graphical abstract