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Quantum cylindrical integrability in magnetic fields
by O. Kubů, L. Šnobl
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ondrej Kubu |
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| Preprint Link: | https://arxiv.org/abs/2210.03468v1 (pdf) |
| Date accepted: | 2023-08-11 |
| Date submitted: | 2022-10-10 06:04 |
| Submitted by: | Kubu, Ondrej |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor. 53 085203] to facilitate the comparison, the cases which may a priori differ yield 2 systems without any correction and 2 with it. In all of them, the magnetic field $B$ coincides with the classical one, only the scalar potential $W$ may contain a $\hbar^2$-dependent correction. Two of the systems have both cylindrical integrals quadratic in momenta and are therefore not separable. These results form a basis for a prospective study of superintegrability.
Published as SciPost Phys. Proc. 14, 032 (2023)
Reports on this Submission
Anonymous Report 1 on 2022-12-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2210.03468v1, delivered 2022-12-23, doi: 10.21468/SciPost.Report.6377
Strengths
1 The paper present a review of some results from ref.16 which consists in a classification of quadratically integrable systems of cylindrical type and involving magnetic field in context of quantum mechanics. This is ageneralisation of some work in the classical context in ref.13. The paper allow some progress under the very broad scope of classifying superintegrable systems with magnetic field. The properties of those models are still largely unknown in terms of connection with special functions in general and related symmetry algebra.
2.The paper present some discussion on similarities/differences between the classical and quantum cases and also on the aspect of separation of variables.
Weaknesses
The paper is short, but the results can be viewed as a first study of quantum integrable with magnetic field of cylindrical type and can be viewed as a starting point of broader study of superintegrable systems in that context. I think this is appropriate for a conference proceeding.
Report
I believe the paper satisfy the journal criteria and appropriate for this proceeding.
Requested changes
I have read in details the paper and it is well written. The results also seems ok. The authors mention why the problem is interesting from point of view of mathematics, mathematical physics and I think the authors could consider in the introduction to point out some applications of integrable/superintegrable systems with magnetic field and in context of physics.