Weak-coupling approximations in non-Markovian transport

Zedler, Philipp; Schaller, Gernot; Kießlich, G.; Emary, Clive; Brandes, Tobias

doi:10.1103/physrevb.80.045309

Cited by 51 publications

(71 citation statements)

References 47 publications

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“…However, except for some special cases [17], nonmarkovian master equations are also not guaranteed to preserve positivity, and corresponding counterexamples can be easily constructed [18]. Technically, master equations with memory can for example be solved efficiently when the bath correlation functions can be approximated by a few decaying exponentials [19].…”

Section: Introductionmentioning

confidence: 99%

Systematic perturbation theory for dynamical coarse-graining

2009

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We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we explicitly show that dynamical coarse-graining unconditionally preserves positivity of the density matrix -even for bath density matrices that are not in equilibrium and also for timedependent system Hamiltonians. By construction, the approach correctly captures the short-time dynamics, i.e., it is suitable to analyze non-Markovian effects. We compare the dynamics with the exact solution for highly non-Markovian systems and find a remarkable quality of the coarse-graining approach. The extension to higher orders is straightforward but rather tedious. The approach is especially useful for bath correlation functions of simple structure and for small system dimensions.

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Section: Introductionmentioning

confidence: 99%

Systematic perturbation theory for dynamical coarse-graining

2009

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“…Recent progress in the development of kinetic equations for the electron transport presents a significant promises in this direction. [39][40][41][42][43][44][45][46][47] Although to fully engage transport kinetic equations with the high level electronic structure calculations we need to transform them to the familiar language of second quantization, creation and annihilation operators, normal ordering, Fock space and vacuum. In this paper paper we develop a systematic scheme to convert and solve quantum kinetic equations in the language of the advanced quantum chemistry.…”

Section: Introductionmentioning

confidence: 99%

Super-fermion representation of quantum kinetic equations for the electron transport problem

Dzhioev

Kosov

2011

The Journal of Chemical Physics

142

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We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-Hermitian Liouvillian in super-Fock space. We transform the Liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.

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“…This state has nice classical properties and yields the exact (non-perturbative) solution for the spin-boson pure dephasing model, but conflicts with some exact quantum solutions -as already exemplified by the singleresonant level model 82,98 . Later-on, we will demonstrate further shortcomings of the BMS approximation.…”

Section: B Coarse-graining Schemesmentioning

confidence: 88%

Transport statistics of interacting double dot systems: Coherent and non-Markovian effects

2009

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We formalize the derivation of a generalized coarse-graining n-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient inclusion of coherences and Lamb shift in counting statistics. As a Markovian example with Lindblad-type density matrices, we consider the Born-Markov-Secular (BMS) approximation which is a special case of the non-Markovian dynamical coarse graining (DCG) approach. For illustration we consider transport through two interacting levels that are either serially or parallelly coupled to two leads held at different chemical potentials. It is shown that the coherences can strongly influence the (frequency-dependent) transport cumulants: In the serial case the neglect of coherences would lead to unphysical currents through disconnected conductors. Interference effects in the parallel setup can cause strong current suppression with giant Fano factors and telegraph-like distribution functions of transferred electrons, which is not found without coherences. We demonstrate that with finite coarse graining times coherences are automatically included and, consequently, the shortcomings of the BMS approximation are resolved.

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Weak-coupling approximations in non-Markovian transport

Cited by 51 publications

References 47 publications

Systematic perturbation theory for dynamical coarse-graining

Systematic perturbation theory for dynamical coarse-graining

Super-fermion representation of quantum kinetic equations for the electron transport problem

Transport statistics of interacting double dot systems: Coherent and non-Markovian effects

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