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Fermionic duality: General symmetry of open systems with strong dissipation and memory
by Valentin Bruch, Konstantin Nestmann, Jens Schulenborg, Maarten R. Wegewijs
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|Authors (as registered SciPost users):||Valentin Bruch · Konstantin Nestmann · Maarten Wegewijs|
|Preprint Link:||https://arxiv.org/abs/2104.11202v1 (pdf)|
|Date submitted:||2021-04-23 17:28|
|Submitted by:||Bruch, Valentin|
|Submitted to:||SciPost Physics|
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 (Schrödinger) 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-Jamiołkowski 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.
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2104.11202v1, delivered 2021-05-29, doi: 10.21468/SciPost.Report.2991
1- Numerous details and various approaches illustrated
2- Presents useful method for simplifying solutions of open quantum dynamics
1 - A bit long and at times difficult to follow
2- Unclear what is relation to previous work
The article is very interesting and will be useful to both experts and people a bit further out of the field because it gives numerous details and reviews lots of previous results.
I think that the main usefulness of the new symmetry comes from the possibility to relate left and right eigenvectors via conjugation and parity transformation and that there are cross-relations in the spectrum. The paper goes into the implication of this transformation for various kinds of quantum dynamics beyond the Lindblad equation.
My main point that I would like the authors to address is to better contrast their work with previous work. More specifically, the Lindblad (Markovian) PT symmetry (Ref. [15,16]). Is the main difference that they work with more general quantum map than the ones generated by the Lindblad master equation? The symmetry they introduce seems also a bit similar to weak symmetries in Lindblad master equations: New J. Phys. 14 073007 (2012).
1 - In figure 5 the authors compare the initial slip approximation with the nonperturbative semigroup for a resonant level model. It would be good to have an explanation in the caption how their novel results come into play in this study.
2 - I would have liked to have seen more examples of their duality being used to help compute physical quantities. I leave it as an optional suggestion to the the authors to include another physical example.
1 - Compare with previous work in more detail
2- Explain caption of figure 5 in relation to their work
- Cite as: Anonymous, Report on arXiv:2104.11202v1, delivered 2021-05-27, doi: 10.21468/SciPost.Report.2983
1- Very clear explanation with plentiful of details.
2- Tackles a very interesting subject, providing a useful guideline to tackle nontrivial open system problems.
1 - Sometimes difficult to follow .
In this article, the authors detail a fermionic duality relation between the evolution of states and those of the observable. Such a relation constrain the dynamics and allows simplifying computations for a wide class of fermionic models.
I have very much enjoyed reading this paper, and I appreciated the effort the authors went into to make the paper accessible to a broad audience, by clearly stating the nature of the problem, how it can be understood, and why it is relevant. As such, I can commend its publication as it stands, although I have some suggestions (below) which the authors may want to consider.
1- A point which I find unclear is the recurring discussion of the non-physicality of the duality mapping. While I get that the map (e.g., $\bar \Pi(t)$) does not correspond to any physical system evolving, this can be seen as just a theoretical artifact and $\bar \Pi(t)$ never actually represent the physics of the system. On the contrary, this duality could be used to simulate "unphysical" systems using physical ones. By appropriately transforming the "physical" observables, one can simulate the non-physical domain. As such, I wonder if the authors have thought about this perspective. Obviously, this is just a suggestion, the article is clear as it is.
Other minor details:
2- The discussion about the conditions (I-III) in Section 3 is not very clear. In particular, it not clear in the following discussions how these three conditions ensure the fermionic duality relation.
3- It is a little confusing how Eq. (41) is derived from Eq. (40). Maybe the discussion about the sum rules can be slightly reformulated to make it more straightforward.
4- Concerning 4.2, I think it is closely related to the discussion in [Phys. Rev. Lett. 124, 190402] about the meaning of quantum jumps for divisible open quantum system dynamics.
5- Some similar "unphysical" modelling for bosonic-like systems have been discussed also in [ Phys. Rev. Lett. 120, 030402 (2018a),Nat Commun 10, 3721 (2019)]. I wonder if there is any connection with this work.
6-Very minor point: in the contourplot, sometimes the quantity plotted is indicated above the plot, some other times next to the colorbar, or it is in the caption. Although it is not a problem, it may be better to keep all the plot consistant.
7- Very minor point: Hermitian is often written as "hermitian". I think the correct spelling is Hermitian.
1 - Maybe comment on the point 1.
2- Clarify point 2.
3- Consider to comment on the other points raised in the report.