dorsal/arxiv
View SchemaSpectral properties on a circle with a singularity
| Authors | Tamas Fulop, Izumi Tsutsui, Taksu Cheon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307002 |
| URL | https://arxiv.org/abs/quant-ph/0307002 |
| DOI | 10.1143/JPSJ.72.2737 |
| Journal | J. of Phys. Soc. Jpn 72 (2003) 2737-2746. |
Abstract
We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.
{
"annotation_id": "2cffd5ca-9f4c-44d6-a11b-a52014d2e382",
"date_created": "2026-03-02T18:02:00.203000Z",
"date_modified": "2026-03-02T18:02:00.203000Z",
"file_hash": "090c1be1f6fea2085cbca6f39814809228422b987245f96e7c95b74eab1ebbeb",
"private": false,
"record": {
"abstract": "We investigate the spectral and symmetry properties of a quantum particle\nmoving on a circle with a pointlike singularity (or point interaction). We find\nthat, within the U(2) family of the quantum mechanically allowed distinct\nsingularities, a U(1) equivalence (of duality-type) exists, and accordingly the\nspace of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus.\nWe explore the relationship of special subfamilies of the U(2) family to\ncorresponding symmetries, and identify the singularities that admit an N = 2\nsupersymmetry. Subfamilies that are distinguished in the spectral properties or\nthe WKB exactness are also pointed out. The spectral and symmetry properties\nare also studied in the context of the circle with two singularities, which\nprovides a useful scheme to discuss the symmetry properties on a general basis.",
"arxiv_id": "quant-ph/0307002",
"authors": [
"Tamas Fulop",
"Izumi Tsutsui",
"Taksu Cheon"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"math-ph",
"math.MP"
],
"doi": "10.1143/JPSJ.72.2737",
"journal_ref": "J. of Phys. Soc. Jpn 72 (2003) 2737-2746.",
"title": "Spectral properties on a circle with a singularity",
"url": "https://arxiv.org/abs/quant-ph/0307002"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1dda175e-0bba-42c4-881c-7d9e08b2b7c9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}