Pattern Formation and Aggregation in Ensembles of Solitons in Quasi One-Dimensional Electronic Systems
Round 1
Reviewer 1 Report
Journal: Symmetry (Section: Physics and Symmetry/Asymmetry; Special Issue: Topological Objects in Correlated Electronic Systems)
Manuscript ID: symmetry-1685172
Type of manuscript: Article
Title: Pattern formation and aggregation in ensembles of solitons in quasi one-dimensional electronic systems
Authors: Petr Karpov, Serguei Brazovskii
Reviewer invited: April 01, 2022
Report submitted: April 05, 2022
The manuscript symmetry-1685172 “Pattern formation and aggregation in ensembles of solitons in quasi one-dimensional electronic systems” by Petr Karpov and Serguei Brazovskii presents a brief review of the results obtained by the Authors in numerical studies of statistical ensembles of solitons and published in papers [“Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field”, Physical Review B 94, 125108 (2016)], [“Phase transitions and pattern formation in ensembles of phase-amplitude solitons in quasi-one-dimensional electronic systems”, Physical Review E 99, 022114 (2019)], and [“Modeling of networks and globules of charged domain walls observed in pump and pulse induced states”, Scientific Reports 8, 4043 (2018)].
In Section “1. Introduction: Confinement and phase transitions in ensembles of solitons”, the Authors give overall pretty good introduction to the research area: the motivation of the research is explained, its place in the current scientific agenda is shown, and relevant papers on this topic are cited.
Section “2. Discrete symmetry: solitons in doubly-degenerate systems” deals with the case of a discrete symmetry breaking (the double degeneracy, to be more precise). In this case, emergence of solitons named “kinks” is possible. Connection with the Ising model is shown, results of the numerical simulations are presented.
In Section “3. Pattern formation in ensembles of phase-amplitude solitons for a complex order parameter”, evolution of ensembles of solitons via a sequence of phase transitions is described.
Finally, In Section “3.4. Conclusions” the Authors summarize and give some concluding remarks. The list of references contains 24 items and is quite adequate.
The results presented/reviewed in the manuscript are new and could be of interest to the scientific community. However, I have several minor suggestions/comments that, I believe, must be addressed before the publication of the manuscript could be recommended. The list of my remarks and suggestions, is given below. I would like the Authors to accurately answer each point. If the Authors agree with my remark, I ask them to amend the text of the manuscript accordingly. In all cases when the Authors do not agree with my suggestion, I kindly ask them to give a reasoned answer.
After the Authors address all my comments and suggestions, I will be happy to give a final recommendation regarding the possibility of publication of this paper in “Symmetry”. (I also believe that in the case of a proper revision of the manuscript, it can be published without my re-review.)
List of my comments and recommendations to the Authors.
- It is somewhat strange that Section “3.4. Conclusions” is a subsection of Section “3. Pattern formation in ensembles of phase-amplitude solitons for a complex order parameter”. I suggest to make the Conclusion a separate section with number 4.
- I recommend to check punctuation after equations. In many places dots and commas are missing. I suggest to follow the principle that formula or equation is a part of the sentence.
- Line 230: Abbreviation ICDW has already been introduced on page 2.
- Line 242: Abbreviation FFLO must be clarified.
- Line 254: Abbreviation SC should be clarified.
- Line 283: Abbreviation MF should be clarified.
- Line 335 (or 366): Abbreviation BKT should be clarified.
- Line 396: Abbreviation MC has already been introduced above.
- The Authors mention forces acting between kinks. Can the Authors give some comments on these forces within the reviewed studies? There is a number of papers which deal with such forces, see, e.g., the following papers (and references related to kink-antikink interactions, collisions, scattering and forces therein):
https://doi.org/10.1016/j.physletb.2021.136361
https://doi.org/10.1016/j.aop.2021.168739
Author Response
We thank the reviewer 1 for the careful reading of our manuscript and for a number of useful comments and advices.
All of them have been taken into account which contributed to the quality and readability of the article.
1. It is somewhat strange that Section “3.4. Conclusions” is a subsection of Section “3.
Pattern formation in ensembles of phase-amplitude solitons for a complex order parameter”.
I suggest to make the Conclusion a separate section with number 4.
Response: Corrected, page 14, line 444.
2. I recommend to check punctuation after equations. In many places dots and commas are missing.
I suggest to follow the principle that formula or equation is a part of the sentence.
Response: Done throughout all equations.
3. Line 230: Abbreviation ICDW has already been introduced on page 2.
Response: The repeating definition of ICDW is deleted.
4. Line 242: Abbreviation FFLO must be clarified.
Response: Corrected, page 7, line 247.
5. Line 254: Abbreviation SC should be clarified.
Response: The abbreviation SC was deleted in favor of the full name “superconductivity”.
6. Line 283: Abbreviation MF should be clarified.
Response: The abbreviation MF was deleted in favor of the full name “mean-field”.
7. Line 335 (or 366): Abbreviation BKT should be clarified.
Response: The abbreviation BKT was defined as “Berezinskii–Kosterlitz–Thouless” at page 10, line 350;
new references [19,20] has been added for this purpose.
8. Line 396: Abbreviation MC has already been introduced above.
Response: The abbreviation MF was deleted in favor of the full name “mean-field”.
9. The Authors mention forces acting between kinks.
Can the Authors give some comments on these forces within the reviewed studies?
There is a number of papers which deal with such forces, see, e.g., the following papers
(and references related to kink-antikink interactions, collisions, scattering and forces therein):
https://doi.org/10.1016/j.physletb.2021.136361 https://doi.org/10.1016/j.aop.2021.168739
Response: The necessary discussion has been presented in page 3, lines90-94;
new references [1,15] have been added for this purpose.
Reviewer 2 Report
This paper contains a very complete and rigorous study of systems of solitons, in the context of quasi-one-dimensional electronic systems which give rise to microscopic solitons taking roles of carriers of charge or spin giving rise to phase vortices, amplitudes solitons, and their combinations, then the authors find that long-range ordering in dimensions above one imposes super-long-range confinement forces upon the
solitons, leading to a sequence of phase transitions in their ensembles, then they study behavior t high temperature which enforces the confinement of solitons into topologically bound complexes: pairs of kinks and several other effects, all very interesting, studied in a very serious manner, I definitelly recommend this paper for publication
Author Response
We thank the reviewer 2 for the totally positive estimation of our article
