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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 | |
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| Preprint Link: | https://arxiv.org/abs/2210.04973v2 (pdf) |
| Date accepted: | 2023-02-14 |
| Date submitted: | 2022-12-21 13:50 |
| Submitted by: | Wegewijs, Maarten |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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)