Violation of Onsager's theorem in approximate master equation approaches

Seja, Kevin Marc; Kiršanskas, Gediminas; Timm, Carsten; Wacker, Andreas

doi:10.1103/physrevb.94.165435

Cited by 11 publications

(17 citation statements)

References 37 publications

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“…However, similarly as in Ref. [48] the violation is of higher order in than the currents, and for sufficiently weak coupling no problem arises. We quantify this violation by considering the ratio of the peak value O,peak = max V g , | O,peak (V g , )| to the peak value L 1,peak = max V g , |L 1 (V g , )| in the (V g , ) parameter space.…”

Section: B Onsager's Relationsupporting

confidence: 65%

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Phenomenological position and energy resolving Lindblad approach to quantum kinetics

2018

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A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities.

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Section: B Onsager's Relationsupporting

confidence: 65%

“…[48]). This raises the following question: Does our proposed PERLind scheme satisfy Onsager relations?…”

Section: B Onsager's Relationmentioning

confidence: 99%

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

2018

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“…However, negative occupations are rare compared to the first-order approaches addressed below and occur only for strong couplings. Similarly, the deviations from Onsager's theorem are of third order in the rates (Γ 3 ) as shown in [57]. Thus these features may be used to monitor the validity of results with increasing tunnel coupling.…”

Section: Pros (+) and Cons (-) Of This Approachmentioning

confidence: 84%

“…Also the temperature T needs to be larger than any Kondo temperature T K in the system [11,19,56]. -Can violate the positivity of the reduced density matrix Φ [0] and does not satisfy the Onsager relations [57], when H Coulomb 0. However, negative occupations are rare compared to the first-order approaches addressed below and occur only for strong couplings.…”

Section: Pros (+) and Cons (-) Of This Approachmentioning

confidence: 99%

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QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Wacker

Pedersen

Karlström

et al. 2017

Computer Physics Communications

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QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), firstorder Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches. Keywords: Open quantum systems, Quantum dots, Anderson-type model, Coulomb blockade, Python Program summaryProgram Title: QmeQ Licensing provisions: BSD 2-Clause Programming language: Python External libraries: NumPy, SciPy, Cython Nature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads. Solution method: Exact diagonalisation of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach. Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

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Are Onsager's reciprocal relations necessary to apply Thermodynamic Extremal Principles?

Hackl

Fischer

Zickler

et al. 2020

Journal of the Mechanics and Physics of Solids

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Violation of Onsager's theorem in approximate master equation approaches

Cited by 11 publications

References 37 publications

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Are Onsager's reciprocal relations necessary to apply Thermodynamic Extremal Principles?

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