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Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

by Lara C. Ortmanns, Maarten R. Wegewijs, Janine Splettstoesser

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Submission summary

Authors (as registered SciPost users): Maarten Wegewijs
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-02-14
Date submitted: 2022-12-21 13:50
Submitted by: Wegewijs, Maarten
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -- so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -- covering both the repulsive and attractive case -- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

List of changes

1. Introduction was shortened + revised to improve accessibility for non-expert reader

2. After Eq. (22): relation to general duality pointed out.

3. After Eq. (43b): a missing substitution mentioned.

4. After Eq. (89): references to earlier worked-out examples highlighted.

5. Summary: material cut from introduction merged + outlook paragraph extended.

6. References [8] and [39] were added

Published as SciPost Phys. 14, 095 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-1-9 (Invited Report)


The revised version of the manuscript presents some improvements, in terms of readability and completeness, upon the already fine first version. For this reason I recommend publication in SciPost Physics.

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Anonymous Report 1 on 2022-12-22 (Invited Report)


The authors response is clarifying and the modifications made to the introduction and conclusions in the revised version of the manuscript greatly increases its readability. Hence, I recommend it for publication without further requests.

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