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Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz

by Jan C. Zill, Tod M. Wright, Karen V. Kheruntsyan, Thomas Gasenzer, Matthew J. Davis

This Submission thread is now published as SciPost Phys. 4, 011 (2018)

Submission summary

As Contributors: Matthew Davis · Thomas Gasenzer
Arxiv Link: (pdf)
Date accepted: 2017-12-23
Date submitted: 2017-11-20 01:00
Submitted by: Davis, Matthew
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approaches: Theoretical, Computational


We use the coordinate Bethe ansatz to study the Lieb-Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.

Ontology / Topics

See full Ontology or Topics database.

Attractive Bose gas Bethe Ansatz Coordinate Bethe Ansatz (CBA) Dynamical correlation functions Lieb-Liniger model One-dimensional Bose gas Quantum quenches Relaxation dynamics

Published as SciPost Phys. 4, 011 (2018)

Author comments upon resubmission

Dear editor,

We appreciate the time and effort the three referees have invested in reading our manuscript, and the resulting suggestions for clarification and improvement. We have made changes in response to the majority of these suggestions, and explained our reasons for not making changes for those that remain in our responses to the reports. We believe that the manuscript has improved as a result.

We apologise for the length of time it has taken us to make the revisions. We hope that our work can now be accepted for publication.

Best regards,
Jan Zill, Tod Wright, Karen Kheruntsyan, Thomas Gasenzer, Matthew Davis.

List of changes

Summary of changes in response to referee reports
(full details in our individual responses to the reports)

+ Expanded the introduction to make a more explicit connection with our earlier work, and more detail about the contribution of this paper relative to others.

+ Added further explanation regarding the hump in momentum distributions for strongly interacting systems in Fig 2(c).

+ Added a summary to the end of section 4 and section 5 to highlight the key results.

+ Added text explaining the reason for the mean-field solution for \gamma = −0.21 in Fig 1(a) being broader than exact solution.

+ Revised the text regarding the k^-4 scaling of the momentum in Fig. 2(c).

+ Commented on the more regular nature of $g^3$ relative to $g^2$ in Fig 5.

+ Expanded on the comparison with the ideal gas correlation function in Fig. 11(b).

Additional revisions to the manuscript:

+ Sec. 1: We removed a citation to "G. Dvali et al., Scrambling in the black hole portrait" as upon revisiting this we decided it does not bear on the point we are making in the text.

+ Sec. 3.1: We corrected references to "pink diamonds" in Fig. 1 to "pink triangles".

+ Sec. 4.2, we replaced: "energy difference between the two-body bound state {n_j} = {2,0} and the three-body bound state {n_j} = {1,0}" with "energy difference between the three-body bound state {n_j} = {1,0} and the predominant two-body bound state {n_j} = {2,0}".

+ Sec. 5, below Eq. (14), we added a sentence: "We note that in practice the sum in Eq. (14) runs over a finite set of energy eigenstates with populations |C_{lambda_j}|^2 exceeding some threshold value." (As although this detail should be clear enough at this point, it should be noted explicitly as in our previous Refs. [32, 33].)

+ Fig. 10, we replaced "strong-coupling thermodynamic-limit prediction for g(2)DE(0)" with the more accurate "strong-coupling (order-1/gamma^3) thermodynamic-limit prediction for the stationary value of g(2)(0)".

+ Appendix A: We have slightly reordered the text around equations (15)-(17) for clarity and everywhere replaced the symbol theta_0 with a capital Theta.

+ Appendix B: We added citations to references [42,43] for the concept of the string deviations.

+ Appendix B.3, above Eq. (32) we added the words "in the limit of small string deviations" to make this point more clear (and accurate).

+ We also made a few other very minor changes to wording and punctuation throughout the manuscript to make the presentation more clear.

Reports on this Submission

Anonymous Report 2 on 2017-12-12 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1705.09168v2, delivered 2017-12-12, doi: 10.21468/SciPost.Report.293


I am satisfied with the current version of the paper, I think that the authors made all the possible efforts to improve it and the numerical results presented are the best they can produce. So I recommend this paper for publication in Scipost.

  • validity: high
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2017-12-6 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1705.09168v2, delivered 2017-12-06, doi: 10.21468/SciPost.Report.290


I'm satisfied with the authors' response and changes in the manuscript.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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