SciPost Submission Page
Beyond-mean-field analysis of the Townes soliton and its breathing mode
by Dmitry S. Petrov
Submission summary
| Authors (as registered SciPost users): | Dmitry Petrov |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202412_00042v2 (pdf) |
| Date submitted: | April 15, 2025, 7:46 p.m. |
| Submitted by: | Petrov, Dmitry |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
By using the Bogoliubov perturbation theory we describe the self-bound ground state and excited breathing states of $N$ two-dimensional bosons with zero-range attractive interactions. Our results for the ground state energy $B_N$ and size $R_N$ improve previously known large-$N$ asymptotes and we better understand the crossover to the few-body regime. The oscillatory breathing motion results from the quantum-mechanical breaking of the mean-field scaling symmetry. The breathing-mode frequency scales as $\Omega\propto |B_N|/\sqrt{N}$ at large $N$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
I am grateful to the Referees for their careful reading of the manuscript, for their very positive opinion, and for valuable comments and suggestions. I have modified the manuscript according to their suggestions. I hope that you find the revised version suitable for publication.
Sincerely,
Dmitry Petrov
List of changes
The derivation of the mean-field action is rewritten and I discuss the mean-field evolution in more detail (Sec.2).
The hierarchy of energy scales and the logic behind the perturbative expansion are explained in a new paragraph in the end of Sec.2.
I modified the derivation of the formula for the beyond-mean-field correction (Sec.3). The regularization is now introduced from the very beginning, the logarithmic dependence on the cutoff is derived explicitly, and the meaning of xi is explained more clearly.
I modified the discussion on the adiabaticity in Sec.4. I added a few references as recommended by Referee 1.
A few misprints are fixed.
No modification of the results or figures.
Current status:
Reports on this Submission
Strengths
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The manuscript highlights subtle issues in the quantum dynamics of cold atomic clouds
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The general idea is (relatively) straightforward to follow
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The problem is potentially of high relevance in view of next experiments
Weaknesses
- No longer applicable. The main weaknesses have been solved
Report
A couple of minor optional (but warmly welcome) further suggestions:
-the abstract is still a bit technical. E.g., I don't like having formulas in there. The author may consider reformulating it in a more accessible way. Also the last paragraph of the intro may be made more accessible and slightly more detailed.
-on pag.5, I am puzzled by the formula |g-gc|~g^2<<|gc|. I don't see what it means to formally set g=gc. The author should spend a few words to explain what he has in mind.
-when discussing after eq.(27) the condition for adiabaticity, the author mentions the risk of non-adiabatic features at large R, but says nothing on what may happen at smnall R. Even though the gap is here the largest, I see from Fig.1 that the effective potential grows very fast. I am therefore wondering if the strong acceleration felt around this left turning point may induce any additional adiabatic effect.
Requested changes
- Take into due consideration my suggestions for (optional) revisions
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)