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=−∞.
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.
We discuss the equivalence of two nonequilibrium kinetic theories that describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a harmonic trap. The second-order kinetic equations of Walser et al. [Phys. Rev. A 63, 013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum Boltzmann equation in the low- and high-temperature limits, respectively. These kinetic equations thus describe the system in equilibrium (finite temperature) as well as in nonequilibrium (real time). We have found this theory to be equivalent to the nonequilibrium Green's function approach originally proposed by Kadanoff and Baym and more recently applied to inhomogeneous trapped systems by Imamovi\ifmmode \acute{c}\else \'{c}\fi{}-Tomasovi\ifmmode \acute{c}\else \'{c}\fi{} and Griffin [in Progress in Nonequilibrium Green's Functions, edited by M. Bonitz (World Scientific, Singapore, 2000), p. 404].
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