SciPost Submission Page

Fermionic duality: General symmetry of open systems with strong dissipation and memory

by Valentin Bruch, Konstantin Nestmann, Jens Schulenborg, Maarten R. Wegewijs

Submission summary

As Contributors: Valentin Bruch · Konstantin Nestmann · Maarten Wegewijs
Arxiv Link: (pdf)
Date accepted: 2021-08-31
Date submitted: 2021-06-28 10:51
Submitted by: Bruch, Valentin
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schr\"odinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamio{\l}kowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

Published as SciPost Phys. 11, 053 (2021)

List of changes

* The explanation of the relation to other works has been extended and moved to a dedicated paragraph in Section 6 (p. 35f.).
* page 4: The explanation of the special case of fermionic duality in the weak coupling limit has been clarified.
* page 6: The discussion of the unphysical properties of the dual propagator has been extended. It is now mentioned that only the unphysical dual system can lead to the unconventional insights of fermionic duality.
* page 12: It is now clarified that the assumptions (I)-(III) are required to derive the duality relation, but are not discussed in this work.
* page 17: The explanation of Eq. (41) has been corrected. It requires the orthonormality of the canonical measurement operators.
* page 27: Footnote 20 has been added and provides a connection to the weak coupling duality.
* page 32: The caption of Figure 5 has been rewritten to clarify the role of fermionic duality in this figure.
* page 35f.: Section 6 has be restructured. It now contains a summary, the relation to other works and the outlook as separate parts. The goal of the duality ("simplifying a calculation given a method of choice") is now stated more explicitly.
* page 36: The outlook has been rewritten and adapted to the new structure of Section 6.

Reports on this Submission

Anonymous Report 1 on 2021-8-26 (Invited Report)


The authors have addressed my remarks and I recommend publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
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