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Efficient flow equations for dissipative systems
by Gary Ferkinghoff, Götz S. Uhrig
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Gary Ferkinghoff · Götz Uhrig |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2203.15532v2 (pdf) |
| Date accepted: | 2022-09-15 |
| Date submitted: | 2022-07-26 05:30 |
| Submitted by: | Ferkinghoff, Gary |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.
Author comments upon resubmission
first of all, we like to point out that the first author has changed his name following his marriage. He would like to change his name on the manuscript from “Gary Ferkinghoff” to “Gary Schmiedinghoff”.
We thank you for taking up the time-consuming burden to provide two meaningful reports. We read both of them closely and modified our manuscript according to all the uttered constructive criticisms. In this way, the manuscript has improved and we think that it is now ready for publication.
Referee 1 sees a number of strengths (“well written manuscript”, “detailed compa¬rison”, “new GPC generator”). But she/he identified also three weaknesses (“no new physics”, “analytical handling”, “literature”) and missed a “groundbreaking theoretical and computational discovery” so that the recommendation is rather for SciPost Physics Core than for SciPost Physics.
We added the requested literature and point out that most of the studied examples already treat systems in second quantization already. We appended also analytical solutions where available so that two of three weaknesses are removed. As for new physics, we point out that our results provide novel insights in the renormalization of Lindbladians which partly differ significantly from the renormalization of non-Hermitian Hamiltonians. But we stress that the main aim of our study is to pave the way for new theoretical tools which have to be bench-marked with known results. Further¬more, we did not only introduce a novel generator scheme, but provided the first compre¬hen¬sive comparison of generators for open quantum systems with respect to their truncation properties; for instance, no such discussion is present in Rosso et al. (Ref. 1). This is the second key point of our manuscript. Its novelty in the field of dissipative quantum systems may have been underestimated by Referee 1.
Referee 2 is extremely positive about the manuscript: “The paper is clearly written and shows very good understanding of the flow equation methodology. It will be a very good resource for readers who want to apply this machinery to the many important problems in open quantum systems.” Hence, except for an amendment which we now have introduced in the revised manuscript, she/he “recommend[s] that the paper should be published once the above comment regarding the transformation of observables is included”.
All in all, we feel that our contribution provides a new approach in the recently booming field of quantum dissipation and non-equilibrium physics which clearly has the potential for a humongous variety of follow-up work. For this reason, we feel that our manuscript fits nicely to SciPost Physics.
We are looking forward to the advancing review process.
Yours sincerely
Gary Schmiedinghoff and Götz Uhrig
List of changes
1) Author name "Gary Ferkinghoff" was changed to "Gary Schmiedinghoff"
2) References 41, 42, 53, 60, 61 and 62 were added in the introduction
3a) In Sec. 2.1 a sentence was added in the fourth line, which points out that all relevant observables are transformed to effective observables in the same basis as the effective Hamiltonian
3b) Equation (3) and a short sentence in front of Eq. (3) were added
4a) In Sec. 2.2 a sentence was added two lines after Eq. (4), which points out that the concrete definition of Q is specific to the problem
4b) Equation (5) and an introductory sentence were added
4c) The text between Eq. (5) and Eq. (6) was slightly edited and a sentence explaining H+ and H- in more detail were added
5) In Sec 2.3 equation (13) was extended with the definition of the observable flow
6a) At the end of Sec. 4.2.1 a sentence stressing that the calculation is performed in second quantization was added
6b) Appendix C was added, which covers the analytical solution of the model in Sec. 4.2 and the analytical solution of an additional observable
6c) At the end of Sec. 4.2.3 the new appendix C is referenced
7a) In Sec. 4.4.1 after Eq. (67) a sentence stressing that the calculation is performed in second quantization was added
7b) Appendix D was added, which covers analytical properties of the flow in Sec. 4.4
7c) In front of Eq. (69) the new appendix D is referenced
Published as SciPost Phys. 13, 122 (2022)
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2022-9-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2203.15532v2, delivered 2022-09-07, doi: 10.21468/SciPost.Report.5657
Report
I have read the authors reply and their updated manuscript.
The authors have addressed the majority of the points that I raised. In particular the authors have added new material and analytical insights that could help developing the dissipative flow equation as a semi-analytical approach - rather than a brute force numerical method. The presentation has been also improved and so the review of the literature.
Based on the Authors reply and new material I am convinced that the criteria for publication in SciPost Physics have been met, so I am happy to recommend the paper for publication.