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_00042v3 (pdf) |
| Date accepted: | June 10, 2025 |
| Date submitted: | May 28, 2025, 1:09 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 breathing oscillations, absent on the mean-field level, result from the quantum-mechanical breaking of the mean-field scale 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 thank the referees for the reports. I slightly modify the manuscript in response to Referee #1. I hope you find it suitable for publication.
Sincerely,
Dmitry Petrov
List of changes
1) In the abstract I replaced the sentence
"The oscillatory breathing motion results from the quantum-mechanical breaking of the mean-field scaling symmetry."
by
"The breathing oscillations, absent on the mean-field level, result from the quantum-mechanical breaking of the mean-field scale symmetry."
2) In the last paragraph of the introduction I added two sentences:
"We thus predict the preexponential factor in the dependence of the ground state energy on the particle number."
and
"We also make a few conjectures concerning the next-order correction to the soliton's energy and the nature of its excitation spectrum."
3) After Eq.(12) in the paragraph starting with "The equation of motion corresponding..." I replaced R(t)^2 by R^2(t).
4) On page 5 in the paragraph starting with "A technical difficulty with..." I replaced the phrase "to formally set g = g_c" by "to use the approximation g = g_c" and added the sentence
"Distinguishing between g and g_c in this case would exceed the Bogoliubov accuracy."
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)