SciPost Submission Page
Tunneling with physics-informed RG flows in the anharmonic oscillator
by Alfio Bonanno, Friederike Ihssen, Jan M. Pawlowski
Submission summary
| Authors (as registered SciPost users): | Friederike Ihssen |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202510_00005v1 (pdf) |
| Date submitted: | Oct. 6, 2025, 11:49 a.m. |
| Submitted by: | Friederike Ihssen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We solve the anharmonic oscillator using physics-informed renormalisation group (PIRG) flows, focusing on the weak coupling regime dominated by instanton-induced tunnelling processes. We demonstrate that the instanton physics underlying the exponential suppression of the energy gap is already captured at the first order of the derivative expansion within the PIRG framework. The key advances of this work are the implementation of a ground-state expansion in the PIRG flow and the adoption of high-precision Galerkin-based numerics. Our determination of the decay constant, $ a_{\mathrm{inst}} = 1.910(2) $, agrees quantitatively with the analytic value $ a_{\mathrm{inst}} = 1.886 $, differing by only $1\%$. While the present formulation relies on a heuristic mapping that will be systematically refined in future extensions of the PIRG approach, these results already highlight the remarkable ability of the method to capture non-perturbative quantum phenomena within relatively simple truncations.
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
Furthermore, we have added multiple references using the ground-state expansion to give a more extensive overview of literature.
List of changes
We have added multiple references using the ground-state expansion (mainly sec III.B), highlighted in red.
Changes in response to the referees (highlighted in orange): - We have restructured sec III.A: Eq. (10) was changed to (13) and we have added text for (14). Eq. (16) and all equations referring to it are moved to App.B. We clarified that knowing (14) is not relevant for the remainder of the paper at sec. III and sec V.A. - We have also added a paragraph in the vicinity of eq. (32) and (33) (formerly 35) and stressed the heuristic nature of the mapping in prominent places of the manuscript (Introduction, Conclusion, Abstract). - We provided a reference to other reconstruction methods [19]. - We have corrected all typos. - We have added Appendix D.3. - We have reformulated the statement regarding the Wetterich eq. at the end of sec. IV and expanded on applications in the PT RG. - We have added a brief statement at the beginning of sec V.B concerning the lacking analysis in terms of $\Delta E$.
Current status:
Reports on this Submission
Strengths
1- The paper exploits a recently developed method and a particular expansion (the ground state expansion) to simplify the study of strongly non-perturbative regimes, by means of Renormalization group flow techniques. 2- The suggestion of an original observable, in principle simpler to compute with large accuracy, in order to point out the non-perturbative features of the analysed problem. 3- The use of a precise numerical approach, crucial in the resolution of the flow equations.
Weaknesses
1- The method, even if simpler than the straightforward resolution of the two coupled PDEs, still looks rather involved.
2- Although there is an evidence that the present approach produces excellent results about one observable, it is still difficult to highlight the overall improvement, since a direct confrontation with the existing techniques is still lacking.
Report
At the same time, I am disappointed about the impossibility of improving on the comparison between the present approach and the old numerical computation of the energy gap, which would have shown the actual progress achieved. However I agree that this is quite a difficult task, outside of the scope of the present work, and postponable to future works.
In view of these comments, I think that the paper is publishable in the present form.
Nevertheless, in the "Requested changes" below, I just quote some typos I
spotted in the modified parts of the paper, that could certainly have been
avoided by a more careful editing.
Requested changes
Beginning of page 2 (sentence in orange) :
Within the PIRG setup two are.. --> Within the PIRG setup, the two are..
End of Subsection III A , page 4 (sentence in orange):
This new observable that is tailor-made for predicting the prefactor..
--> This new observable is tailor-made for predicting the prefactor..
Last sentence in Appendix D 3. :
"In the fluid-dynamical framework we are presently using
resolving a .. "
one verb must be cancelled.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)