Systematic perturbation theory for dynamical coarse-graining

Schaller, Gernot; Zedler, Philipp; Brandes, Tobias

doi:10.1103/physreva.79.032110

Cited by 35 publications

(43 citation statements)

References 42 publications

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“…For our specific model, following reference 38 we obtain = 2πδ(ω − ǫ d ) we see that for large times the coarse graining method yields the same steady state density matrix as the two other approximations. Also for current and Fano factor we have reproduced the results of the MME.…”

Section: B Dynamical Coarse Graining (Dcg)supporting

confidence: 51%

Weak-coupling approximations in non-Markovian transport

et al. 2009

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We study the transport properties of the Fano-Anderson model with non-Markovian effects, which are introduced by making one tunneling rate energy-dependent. We show that the non-Markovian master equation may fail if these effects are strong. We evaluate the stationary current, the zero frequency current noise and the occupation dynamics of the resonant level by means of a quantum master equation approach within different approximation schemes and compare the results to the exact solution obtained by scattering theory and Green's functions.

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Section: B Dynamical Coarse Graining (Dcg)supporting

confidence: 51%

Weak-coupling approximations in non-Markovian transport

et al. 2009

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“…This proposal has been successfully applied to several situations [40][41][42][43], and it can be seen as a "refined" weak coupling limit [43]. However, as far as we know [42], low attention has been payed to study whether or not it accounts for the non-Markovian features expected at the short time scale.…”

Section: Introductionmentioning

confidence: 99%

Refined weak-coupling limit: Coherence, entanglement, and non-Markovianity

Rivas¹

2017

Phys. Rev. A

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We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals whereas the former not, despite the induced dynamics is fully incoherent. In addition, the evolution presents "quasi-eternal" nonMarkovianity, becoming non-divisible at any time period where the system evolves qualitatively. Furthermore, the method allows for an exact derivation of a master equation that accounts for a reversible energy exchange between system and environment. Specifically, this is obtained in the form of a time-dependent Lamb shift term.

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“…Regarding the dynamical coarse-graining approach 81,98 , these findings demonstrate that for the serial double dot considered here, the coarse-graining time must not be sent to infinity. To obtain non- Fig.…”

Section: B Coarse-graining Resultsmentioning

confidence: 76%

“…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%

“…For example, in order to approximate the short-time dynamics of the exact solution well (and thereby also the dynamics of the non-Markovian master equation), τ should scale linearly with the physical time. In contrast to conventional Markovian master equations, the dynamical coarse-graining method (DCG) 81,98 therefore formally solves all coarse-graining master equations (14) and then fixes the coarse-graining time parameter τ = t in the solution…”

Section: B Coarse-graining Schemesmentioning

confidence: 99%

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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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Systematic perturbation theory for dynamical coarse-graining

Cited by 35 publications

References 42 publications

Weak-coupling approximations in non-Markovian transport

Weak-coupling approximations in non-Markovian transport

Refined weak-coupling limit: Coherence, entanglement, and non-Markovianity

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

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