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The complete trans-series for conserved charges in the Lieb-Liniger model
by Zoltán Bajnok, János Balog, Ramon Miravitllas, Dennis le Plat, István Vona
Submission summary
| Authors (as registered SciPost users): | János Balog · Dennis le Plat |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00022v2 (pdf) |
| Date submitted: | Dec. 17, 2025, 6:44 p.m. |
| Submitted by: | Dennis le Plat |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We determine the complete trans-series solution for the (non-relativistic) moments of the rapidity density in the Lieb-Liniger model. The trans-series is written explicitly in terms of a perturbative basis, which can be obtained from the already known perturbative expansion of the density by solving several ordinary differential equations. Unknown integration constants are fixed from Volin's method. We have checked that our solution satisfies the analytical consistency requirements including the newly derived resurgence relations and agrees with the high precision numerical solution. Our results also provides the full analytic trans-series for the capacitance of the coaxial circular plate capacitor.
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
We thank the referees for their careful reading of the manuscript and their useful suggestions. We have improved the manuscript in line with their comments. In the following, we address the three requested changes:
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Wherever possible, we updated the references to their published journal versions. However, some references are not yet published, and since the author of [29] deceased, it will probably never be published.
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We added half a page in the introduction to summarize the logical steps of our construction for readers less familiar with earlier works. We also added a pedagogical Appendix with a figure about Volin's method and its implementation in the present context.
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We added a paragraph in the conclusion about the parameter range of the possible observations of the non-perturbative corrections we determined. Unfortunately, we cannot add more about the semi-classical origin of the renormalon contributions. This is one of the biggest open problems of the resurgence field nowadays.
We hope that this sufficiently addresses the points raised by the referees and meets their satisfaction. Yours sincerely, The authors
List of changes
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Wherever possible, we updated the references to their published journal versions. However, some references are not yet published, and since the author of [29] deceased, it will probably never be published.
-
We added half a page in the introduction to summarize the logical steps of our construction for readers less familiar with earlier works. We also added a pedagogical Appendix with a figure about Volin's method and its implementation in the present context.
-
We added a paragraph in the conclusion about the parameter range of the possible observations of the non-perturbative corrections we determined. Unfortunately, we cannot add more about the semi-classical origin of the renormalon contributions. This is one of the biggest open problems of the resurgence field nowadays.