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Annals of Physics

A New Transport Equation for Single-Time Green′s Functions in an Arbitrary Quantum System. General Formalism

Herbert Schoeller

Published Feb 1, 1994• 24 citations
Publisher
DOI
10.1006/aphy.1994.1009

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We present a Green's-function formalism generalized to treat arbitrary time-dependent systems initially prepared with an arbitrary density matrix. On the basis of a simultaneous expansion of the usual real-time development operator and the density matrix, we define a Green's function ordered along an extended contour. In this way we are able to treat real-time many-particle Green's functions and initial correlations on the same footing. Both can be decomposed by Wick's theorem. Thus we may utilize familiar diagrammatic analysis for evaluating the Green's function, and finally arrive at a generalized Dyson's equation. The Green's function can be represented by a (3\ifmmode\times\else\texttimes\fi{}3) matrix, which includes the Green's functions used in the Feynman, Matsubara, and Keldysh theories, if the corresponding statistical average is taken. From a matrix representation of Dyson's equation, a basic set of five coupled equations is derived, which explicitly shows the corrections to the Keldysh theory due to an arbitrary initial many-particle density matrix.
This review deals with the state of the art and perspectives of description of nonequi-librium many-body systems using the nonequilibrium Green’s function (NGF) method. The basic aim is to describe time evolution of the many-body system from its initial state over its transient dynamics to its long time asymptotic evolution. First, we discuss basic aims of transport theories to motivate the introduction of the NGF techniques. Second, this article summarizes the present view on construction of the electron transport equations formulated within the NGF approach to nonequilibrium. We discuss incorporation of complex initial conditions to the NGF formalism, and the NGF reconstruction theorem, which serves as a tool to derive simplified kinetic equations. Three stages of evolution of the nonequilibrium, the first described by the full NGF description,the second by a non-Markovian generalized master equation and the third by a Markovianmaster equation will be related to each other.
This review deals with the state of the art and perspectives of description of nonequilibrium many-body systems using the nonequilibrium Green's function (NGF) method. The basic aim is to describe time evolution of the many-body system from its initial state over its transient dynamics to its long time asymptotic evolution. First, we discuss basic aims of transport theories to motivate the introduction of the NGF techniques. Second, this article summarizes the present view on construction of the electron transport equations formulated within the NGF approach to nonequilibrium. We discuss incorporation of complex initial conditions to the NGF formalism, and the NGF reconstruction theorem, which serves as a tool to derive simplified kinetic equations. Three stages of evolution of the nonequilibrium, the first described by the full NGF description, the second by a non-Markovian generalized master equation and the third by a Markovian master equation will be related to each other.