dorsal/arxiv
View SchemaDeformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
| Authors | Dennis Bonatsos, D. Lenis, P. P. Raychev, P. A. Terziev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311191 |
| URL | https://arxiv.org/abs/quant-ph/0311191 |
| Journal | Progress in Theoretical Chemistry and Physics Vol 12, Advanced Topics in Theoretical Chemical Physics, ed. J. Maruani, R. Lefebvre, and E. Brandas (Kluwer, Dordrecht, 2003) 409-428 |
Abstract
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
{
"annotation_id": "c02e7890-98de-4193-a1d0-d864bec9ce3f",
"date_created": "2026-03-02T18:02:03.230000Z",
"date_modified": "2026-03-02T18:02:03.230000Z",
"file_hash": "7fe7dbb4407176022894b78cca7b02c7489633d02458a76d0078baa0c716ff98",
"private": false,
"record": {
"abstract": "The predictions for the shell structure of metal clusters of the\nthree-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing\ntechniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are\ncompared to the restrictions imposed by the periodic orbit theory of Balian and\nBloch, of electrons moving in a spherical cavity. It is shown that agreement\nbetween the predictions of the two models is established through the\nintroduction of an additional term to the Hamiltonian of the 3D q-HO, which\ndoes not influence the predictions for supershells. This term preserves the\nUq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a\nvariational procedure, analogous to the one leading from the usual harmonic\noscillator to the Morse oscillator by introducing the concept of the Variable\nFrequency Oscillator (VFO).",
"arxiv_id": "quant-ph/0311191",
"authors": [
"Dennis Bonatsos",
"D. Lenis",
"P. P. Raychev",
"P. A. Terziev"
],
"categories": [
"quant-ph"
],
"journal_ref": "Progress in Theoretical Chemistry and Physics Vol 12, Advanced\n Topics in Theoretical Chemical Physics, ed. J. Maruani, R. Lefebvre, and E.\n Brandas (Kluwer, Dordrecht, 2003) 409-428",
"title": "Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory",
"url": "https://arxiv.org/abs/quant-ph/0311191"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "309dbc08-8c20-478e-bc0b-1be6a60f4775",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}