Degeneracies In a Weighted Sum of Two Squares
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908292281794560 |
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| author | Ramesh, Ishan Vinayagam Olshanii, Maxim |
| author_facet | Ramesh, Ishan Vinayagam Olshanii, Maxim |
| contents | This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, $3n_{1}^2+n_{2}^2$, can be realized in more than one way. Our project was inspired by a particular study of two-dimensional quantum billiards [S. G. Jackson, H. Perrin, G. E. Astrakharchik, and M. Olshanii, SciPost Phys. Core 7, 062 (2024)] where the weighted sums of interest represents an energy level with the two integers being the billiard's quantum numbers; there, the 3-fold degeneracies seem to dominate the energy spectrum. Interestingly, contrary to the conventional paradigm, these degeneracies are not caused by some non-commuting symmetries of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degeneracies In a Weighted Sum of Two Squares Ramesh, Ishan Vinayagam Olshanii, Maxim Mathematical Physics Quantum Gases Quantum Physics 81Q80 This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, $3n_{1}^2+n_{2}^2$, can be realized in more than one way. Our project was inspired by a particular study of two-dimensional quantum billiards [S. G. Jackson, H. Perrin, G. E. Astrakharchik, and M. Olshanii, SciPost Phys. Core 7, 062 (2024)] where the weighted sums of interest represents an energy level with the two integers being the billiard's quantum numbers; there, the 3-fold degeneracies seem to dominate the energy spectrum. Interestingly, contrary to the conventional paradigm, these degeneracies are not caused by some non-commuting symmetries of the system. |
| title | Degeneracies In a Weighted Sum of Two Squares |
| topic | Mathematical Physics Quantum Gases Quantum Physics 81Q80 |
| url | https://arxiv.org/abs/2411.02436 |