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arXiv:1605.07517 · Physical review. D/Physical review. D.

Generalized Kadanoff-Baym relation in nonequilibrium quenched models

A. L. M. Britto, Ashok Das, J. Frenkel

Published May 23, 2016• 1 citation
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Abstract

In the context of a broad class of quenched models, we derive a generalized differential form of the Kadanoff-Baym (KB) ansatz which relates the out of equilibrium correlated and spectral Green's functions. This relation holds at any time both before the quench (when it coincides with the fluctuation-dissipation theorem) as well as after it. We also examine, in the context of exactly soluble quenched models, the validity of some of the earlier alternative extensions of the KB ansatz.

DOI
10.1103/physrevd.93.105034

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We derive an exact functional differential relation for the physical Green's function ${\mathit{g}}_{\ensuremath{\lessgtr}}$(1;2) in terms of its retarded and advanced counterparts and the equal-time function ${\mathit{g}}_{\ensuremath{\lessgtr}}$(1;x2{\mathbf{x}}_{2}x2​,t1{\mathit{t}}_{1}t1​). This exact, formal, functional differential relation is a variant of the generalized Kadanoff-Baym GKB ansatz, and we examine the approximations involved in reducing it to the GKB ansatz.
On the basis of the Kadanoff-Baym (KB) version of the time-dependent Green's function method, an Ansatz for the approximation of a spectral function is offered. The Ansatz possesses all the advantages of quasiparticle and extended quasiparticle approximations and satisfies the KB equation for a spectral function in the case of slightly nonequilibrium system when disturbances in space and time are taken into consideration in the gradient approximation. This feature opens opportunities for the microscopic derivation of the Landau kinetic equation for the quasiparticle distribution function of the normal Fermi liquid and provides the widening of these equations' temperature range of validity.
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This chapter considers the closed-time-path Green’s functions approach when specified to equilibrium situations and shows that it offers an alternative to the more standard Matsubara plus analytic continuation procedure for obtaining physical quantities directly in real frequency. In this case, the number of independent components of the single-particle Green’s function (as well as of the related self-energy) reduces considerably, thereby making it easier to solve the Kadanoff–Baym equations. The fluctuation–dissipation theorem and the single-particle spectral function (with its related sum rule) are also considered.
The Generalized Kadanoff--Baym Ansatz with mean-field propagators is increasingly used to simulate non-equilibrium quantum fermionic and bosonic systems. Compared with the full Kadanoff--Baym equations, its mean-field propagators substantially reduce computational cost, enabling simulations with computational effort that scales linearly with propagation time. However, the time-diagonal structure of the Generalized Kadanoff--Baym Ansatz obscures spectral properties within the collision integral of the transport equation. Here, we recover and investigate these hidden spectral properties using the extended Generalized Kadanoff--Baym Ansatz. For a Hubbard cluster, we compare ground-state spectral functions obtained with the extended Generalized Kadanoff--Baym Ansatz against those from standard Kadanoff--Baym equations. At moderate interaction strengths, the spectral functions show good agreement. At large interaction strengths, however, significant deviations emerge, and the spectral function obtained with the extended Generalized Kadanoff--Baym Ansatz becomes negative. These results demonstrate that, despite its computational advantages, the Generalized Kadanoff--Baym Ansatz has important limitations in strongly interacting regimes and may produce unphysical spectral properties when interactions become sufficiently large.