Dynamics of mesoscopic systems: Non-equilibrium Green's functions approach

Špička, Václav; Kalvová, A.; Velický, B.

doi:10.1016/j.physe.2009.08.008

Cited by 7 publications

(12 citation statements)

References 43 publications

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“…In fact, the scheme can be, on this level of generality, restated in the form

ρ ⇌ {G^{R}, G^{A} G^{<}}

which means a bijective relationship between the full double‐time Green's function and a single‐time single particle density matrix. This has been called the Reconstruction Theorem in .…”

Section: Negf Fluctuation Dissipation Theoremsmentioning

confidence: 99%

“…The principle was postulated by Bogolyubov for extended many particle systems. It states that during the free evolution starting from an arbitrarily correlated many-body initial state the interactions conspire to make all correlations decay within the collision duration time we have denoted τ in (23), and further evolution obeys already a quantum kinetic equation. The Bogolyubov principle has been verified computationally for a number of many-body systems.…”

Section: Extended Versus Small But Open Systemsmentioning

confidence: 99%

“…Here, we will deal with the form of Fluctuation-Dissipation Theorem (FDT), which is formulated within the formalism of Non-Equilibrium Green Functions (NEGF) [2,4,[20][21][22][23][24][25][26]. The FDT in equilibrium is equivalent with the Kubo-Martin-Schwinger (KMS) boundary condition, which permits to write all components of the equilibrium one particle NEGF in terms of the spectral density and a thermal factor [2,20,25,26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

Špička

Velický

Kalvová

2017

Fortschritte der Physik

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The Non‐Equilibrium Fluctuation‐Dissipation Theorem (NE FDT) is formulated within the Non‐Equilibrium Green Function (NEGF) formalism. The relation of this theorem to a simplified kinetic theory of non‐equilibrium dynamics of electrons in open quantum systems is discussed. The possibility of such a simplified description is first discussed on non‐equilibrium dynamics of the molecular bridge model represented by calculations of transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island of an Anderson local center type. This model can be treated by using the full set of equations for NEGF, which can be solved numerically. This provides a reference framework for testing the possibility of a simpler and physically more transparent solution based on a Non‐Markovian Generalized Master Equation (GME) as an approximation of the full set of NEGF equations. The advantages and limitations of the use of the Generalized Kadanoff‐Baym Ansatz (GKBA) for this simplified description is demonstrated. The basic question is the range of applicability of this approximation. It turns out that for our specific model the decisive feature is the spectral structure of the tunneling functions of both electrodes and their positioning with respect to the island level depending on the bias and the exchange splitting. Finally, the relation of this simplified description to non‐equilibrium generalization of FDT is shown independently on the chosen model. The connection between the NEGF reconstruction equations and the non‐equilibrium version of FDT is introduced and the possible approximations of this general scheme are discussed.

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“…In fact, the scheme can be, on this level of generality, restated in the form

ρ ⇌ {G^{R}, G^{A} G^{<}}

which means a bijective relationship between the full double‐time Green's function and a single‐time single particle density matrix. This has been called the Reconstruction Theorem in .…”

Section: Negf Fluctuation Dissipation Theoremsmentioning

confidence: 99%

Section: Extended Versus Small But Open Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

Špička

Velický

Kalvová

2017

Fortschritte der Physik

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“…The ways of incorporating complex initial conditions in the NGF methods are already known in several variants. 92,102,110,118,125,129,131,154,167,168,171,[193][194][195][196][197][198][199][200][201][202][203][204][205][206][207][208][209][210] We will discuss various approaches to initial conditions in Sec. 4.…”

Section: Initial Conditionsmentioning

confidence: 99%

Electron systems out of equilibrium: Nonequilibrium Green's function approach

Špička

Velický

Kalvová

2014

Int. J. Mod. Phys. B

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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.

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“…The underlying perturbation scheme would now be the Keldysh expansion. We have proposed 24,26 to join both methods under the name of diachronous techniques.…”

Section: Introductionmentioning

confidence: 99%

Correlated initial condition for an embedded process by time partitioning

2010

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Study of transients in the electron quantum transport by nonequilibrium Green's function often requires an explicit inclusion of correlations at a finite initial time. For processes embedded in a host process, a universal treatment of the correlated initial conditions based on the formalism of partitioning in time allows to express their self-energy including the "irregular" correlation part in terms of the known properties of the host process. This unified formalism also yields the renormalized semigroup property for propagators and the reconstruction equations for the particle correlation function. The Bogolyubov principle of the decay of correlations then permits to buildup a theory of quantum transport equations with finite-time initial conditions.

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Dynamics of mesoscopic systems: Non-equilibrium Green's functions approach

Cited by 7 publications

References 43 publications

Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

Electron systems out of equilibrium: Nonequilibrium Green's function approach

Correlated initial condition for an embedded process by time partitioning

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