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Quantum chaos in a harmonic waveguide with scatterers

by Vladimir Alexander Yurovsky

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Vladimir Yurovsky
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-13
Date submitted: 2023-09-08 11:50
Submitted by: Yurovsky, Vladimir
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of eigenstates can be calculated using modest computational resources. Integrability-chaos transition can be explored as the model chaoticity increases with the number of scatterers and their strengths. The regime of complete quantum chaos and eigenstate thermalization can be approached with 32 scatterers. This is confirmed by properties of energy spectra, the inverse participation ratio, and fluctuations of observable expectation values.

Author comments upon resubmission

I am indeed grateful to the Referees for careful reading of the manuscript and pointing out unclear statements. All their remarks are addressed. The revised manuscript contains necessary clarifications, as well as other corrections in response to the Referee's remarks. Point-by-point response to the remarks is provided in the replies to the referee reports.

List of changes

Discussion of the relationship to [55] (former [54]) and of the new material appeared in the present work is included in the 4th paragraph of the introduction.

The motivation for investigation of the four particular models is discussed below the paragraph containing Eq. (9).

The complexity of the present model and the possible experimental realization is discussed in the two last paragraphs of Sec. 2.

Figs. 7(a) and 9(a) (former 8(a)) are corrected.

New Fig. 8 is included and discussed.

The level spacing ratio is discussed in the last paragraph of Sec. 3 and in the new appendix C.

Figures 11 and 12 (former 10 and 11) are rearranged and new subfigure 11(b) and additional plots in Fig. 12(b) are included.

Discussion of Figs. 11 and 12 is changed and extended.

Captions to figures 12 and 13 specify which data are shared with [55] (former [54]).

All equations are numbered.

The grammar is corrected.

Published as SciPost Phys. 15, 221 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-11-6 (Invited Report)


Having reviewed the author’s response to the referees’ comments and suggested changes, I believe that all comments and areas of concern have been adequately addressed. In particular, the revised manuscript now clearly addresses the relationship of the current paper to Ref. 55, a previously published work by this author on the same topic, as well as improves upon the discussion of results and overall clarity of the initial manuscript.

Therefore, I am now happy to recommend this paper for publication in SciPost Physics.

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

Anonymous Report 1 on 2023-9-11 (Invited Report)


I have reviewed the author's reply to my first report. I believe he has adequately addressed my comments. In particular, he has edited the manuscript so that it better explains the relationship of the current manuscript to Ref. 55, an earlier PRL on this same topic and he has provided some information on the system's chaoticity as a function of both scattering strength and number of scatterers.

I recommend now that it be published in SciPost Physics.

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

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