dorsal/arxiv
View SchemaSymmetries of anisotropic harmonic oscillators with rational ratios of frequencies and their relations to U(N) and O(N+1)
| Authors | Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis, D. Lenis |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9701039 |
| URL | https://arxiv.org/abs/nucl-th/9701039 |
Abstract
The concept of bisection of a harmonic oscillator or hydrogen atom, used in the past in establishing the connection between U(3) and O(4), is generalized into multisection (trisection, tetrasection, etc). It is then shown that all symmetries of the N-dimensional anisotropic harmonic oscillator with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic oscillator with an appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dimensional hydrogen atom, which possesses an O(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the hydrogen atom lead to the symmetries of the N-dim RHO. The opposite is in general not true, i.e. multisections of U(N) do not lead to O(N+1) symmetries, the only exception being the occurence of O(4) after the bisection of U(3).
{
"annotation_id": "721bf0be-b2da-4cc2-b985-1b026abb4cc3",
"date_created": "2026-03-02T18:00:18.951000Z",
"date_modified": "2026-03-02T18:00:18.951000Z",
"file_hash": "cc18b8f108e04605b79f8442e7f32b3a307a76aa76423c278bf477f9a63e899c",
"private": false,
"record": {
"abstract": "The concept of bisection of a harmonic oscillator or hydrogen atom, used in\nthe past in establishing the connection between U(3) and O(4), is generalized\ninto multisection (trisection, tetrasection, etc). It is then shown that all\nsymmetries of the N-dimensional anisotropic harmonic oscillator with rational\nratios of frequencies (RHO), some of which are underlying the structure of\nsuperdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry\nof the corresponding isotropic oscillator with an appropriate combination of\nmultisections. Furthermore, it is seen that bisections of the N-dimensional\nhydrogen atom, which possesses an O(N+1) symmetry, lead to the U(N) symmetry,\nso that further multisections of the hydrogen atom lead to the symmetries of\nthe N-dim RHO. The opposite is in general not true, i.e. multisections of U(N)\ndo not lead to O(N+1) symmetries, the only exception being the occurence of\nO(4) after the bisection of U(3).",
"arxiv_id": "nucl-th/9701039",
"authors": [
"Dennis Bonatsos",
"C. Daskaloyannis",
"P. Kolokotronis",
"D. Lenis"
],
"categories": [
"nucl-th"
],
"title": "Symmetries of anisotropic harmonic oscillators with rational ratios of frequencies and their relations to U(N) and O(N+1)",
"url": "https://arxiv.org/abs/nucl-th/9701039"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b798a8e3-6d13-4808-8969-c314440530d8",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}