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Shape of a sound wave in a weakly-perturbed Bose gas

by Oleksandr V. Marchukov, Artem G. Volosniev

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Oleksandr Marchukov · Artem Volosniev
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-01-15
Date submitted: 2020-11-30 11:30
Submitted by: Marchukov, Oleksandr
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schr\"odinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

Author comments upon resubmission

Dear Editors,

We thank both Referees for their encouraging reports, and valuable suggestions, which helped us to
improve the presentation of our work. The manuscript has been considerably modified to implement the
changes requested by the Referees, see the list of changes below. The changes are marked with blue color in the text
for convenience. We believe that we addressed all the Referees' comments and we hope that the improved
manuscript is ready to be accepted for publication.

Thank you for your time!

Best regards,

List of changes

List of changes that address Report 1.
1. The revised manuscript clarifies the form of Eq. (3), see the discussion that follows this equation.
2. The revised manuscript explains in more detail why the zero and lost modes are neglected in our
analysis, see the discussion after Eq. (7). In short, we do not need these modes to solve the linearized
Gross-Pitaevskii equation, since the considered perturbation does not excite them.
3. The revised manuscript presents an explicit derivation of the Klein-Gordon equation in footnote 3.
The derivation can indeed help the reader, and we thank the Referee for pointing this fact to us.
4. We have rewritten the discussion that follows Eq. (29). The original formulation was not wrong, but
definitely confusing. We thank the Referee for bringing that sentence to our attention.
5. We have added footnote (4) to explain why the boson-impurity interaction does not affect the impurity
in the leading order.

List of changes that address Report 2.
1. The revised version of our manuscript has a discussion on the normalization of the wave function
immediately after Eq. (2).
2. We have added Sec. 2.1 and Fig. 3 to show that our results can also be used to study trapped systems.
We thank the Referee for her/his comment, which helped us to significantly improve our work.

Published as SciPost Phys. 10, 025 (2021)

Reports on this Submission

Anonymous Report 2 on 2020-12-22 (Invited Report)


The authors have taken into account my questions and comments and have modified the manuscript according, therefore I think this work is now suitable for publication in SciPost.

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Anonymous Report 1 on 2020-12-19 (Invited Report)


The authors have replied satisfactorily to my requests and I recommend the publication of the paper in the current version.

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