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

The study of electron transport is easier if the Kadanoff-Baym equations (KBE) are simplified using the Generalized Kadanoff-Baym Ansatz (GKBA). For molecular bridges, GKBA is empirically known to safely work for weak and flat tunneling functions. It fails, if either of the conditions is not satisfied. The case in point is a molecular bridge formed by an Anderson type local center treated in the mean field and linked by tunneling junctions to two ferromagnetic electrodes whose tunneling functions simulate nickel with complex sd structure. Transient magnetic currents under a constant galvanic bias between electrodes are invoked by sudden switching on of both junctions. We consider three tasks: To establish quantitative criteria for the validity of the Ansatz; to develop a practically tractable correction to the Ansatz working beyond its validity range; to obtain Generalized Master Equations (GMEs) for the one-electron distribution following from both GKBA and its corrected form avoiding thus KBE. All three points are resolved by treating first the stationary (non-equilibrium) limit and transferring the results to finite times. The corrections to the Ansatz are obtained as a stationary approximation to the vertex part of the exact reconstruction equations whose free term is the standard GKBA.

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“…The details about the physical domain, in which the standard Ansatz will work are given in ref. . Here, we summarize the conclusions.…”

Section: Modelmentioning

confidence: 66%

Beyond the Generalized Kadanoff–Baym Ansatz

Kalvová

Velický

Špička

2019

Physica Status Solidi (b)

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“…Extensions to the single-level quantum devices have included the spin degree of freedom for the study of spin currents, magnetism and torque [57,[398][399][400][401][402][403], establishing that, e.g., tunneling magnetoresistance may transiently develop negative values, and the electronic interactions may enhance this effect. In this regard, the GKBA reconstruction has been shown to capture the essential features of magnetic tunnel currents [404][405][406][407].…”

Section: Electronic Transportmentioning

confidence: 99%

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

Ridley,

Talarico,

Karlsson

et al. 2022

Preprint

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We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss nonequilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive -encompassing pump-probe scenarios as well as driven quantum systems -we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system.As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one-and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.

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“…The junction is biased by the voltage V = μ L − μ R . More about this model the reader can find in [14,[21][22][23].…”

mentioning

confidence: 99%

Dynamical vertex correction to the generalized Kadanoff-Baym Ansatz

Kalvová¹,

Špička²,

Velický³

et al. 2023

EPL

Self Cite

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The Generalized Kadanoﬀ-Baym Ansatz, used to simplify the non-equilibrium Green’s functions to the kinetic equation for the density matrix, leads to an incorrect dynamics of a system if the selfenergy has a rich energy spectrum. We propose an approximation of the vertex correction which dynamically changes with the density matrix while it beneﬁts from simplicity of stationary propagators. On the molecular bridge between ferromagnetic leads we demonstrate that this simple vertex ﬁxes the failure of the kinetic equation on a negligible computational cost.

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

Cited by 13 publications

References 43 publications

Beyond the Generalized Kadanoff–Baym Ansatz

Beyond the Generalized Kadanoff–Baym Ansatz

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

Dynamical vertex correction to the generalized Kadanoff-Baym Ansatz

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