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Euler-scale dynamical correlations in integrable systems with fluid motion
by Frederik S. Møller, Gabriele Perfetto, Benjamin Doyon, Jörg Schmiedmayer
This is not the current version.
|As Contributors:||Frederik Skovbo Møller · Gabriele Perfetto · Jörg Schmiedmayer|
|Arxiv Link:||https://arxiv.org/abs/2007.00527v2 (pdf)|
|Date submitted:||2020-07-03 02:00|
|Submitted by:||Møller, Frederik Skovbo|
|Submitted to:||SciPost Physics Core|
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref.  by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationarity, inhomogeneous situations, when motion occurs at the Euler scale of hydrodynamics. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time scales, thus providing the first demonstration of validity for the expressions derived in Ref. . We also observe the onset of the Euler-scale limit for the dynamical correlations.
Submission & Refereeing History
- Comment by Anonymous on 2020-11-19
- Comment by Prof. Davis on 2020-11-21
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Reports on this Submission
Anonymous Report 1 on 2020-8-13 Invited Report
- Cite as: Anonymous, Report on arXiv:2007.00527v2, delivered 2020-08-13, doi: 10.21468/SciPost.Report.1917
The manuscript describes applications of a numerical method for calculation of dynamical two-point correlations to several integrable models. The paper can be interesting and useful for specialists in the field. However, I have several remarks. After proper revision, the paper can meet the acceptance criteria.
As the Euler scale is one of the most important concepts used in the paper, it should be defined and discussed in the introduction for the reader’s convenience.
The statement of the lack of thermalization in integrable systems may be misleading and requires more comprehensive discussion. Integrable systems do relax, but the final state is described by the generalized Gibbs ensemble rather than the Gibbs one. Moreover, there exist also incompletely-chaotic systems (see [PRL 106, 025303]), which relax to a state between the initial one and thermal equilibrium. The Authors also should include a discussion of the basic method of description of integrable systems - the coordinate Bethe ansatz, which can provide both correlation functions (see the review [Adv. At. Mol. Opt. Phys. vol. 55, 61]) and nonequilibrium dynamics (see, e.g., [PRL 119, 220401 (2017)]).
The relativistic sinh-Gordon model is considered only in Appendix B, although application of the method to this model is mentioned in the introduction. I don’t see a reason why the Authors decided don’t present the content of this appendix as a section in the main part.
P. 7: Probably, “which much be chosen” should be “ which must be chosen”
P. 10: A reference to the definition of the Lambert W function should be included. E.g., it can be dlmf.nist.gov if the Author’s definition is indeed the same.
Sec. 4.2: The Authors demonstrate only the examples where the approximation is working perfectly. It would be instructive to present also the examples when the approximation starts to fall, showing to the readers the applicability limits of the approximation.
Sec. 4.2: The direct and indirect correlations are undefined (these terms are also used previously, but I didn't find the definition). Probably, this means the contributions of the direct and indirect propagation, but the terms should be defined unambiguously.