dorsal/arxiv
View SchemaSolvable PT-symmetric model with a tunable interspersion of non-merging levels
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410196 |
| URL | https://arxiv.org/abs/quant-ph/0410196 |
| DOI | 10.1063/1.1925249 |
| Journal | J.Math.Phys. 46 (2005) 062109 |
Abstract
We study the spectrum in such a PT-symmetric square well of a diameter L where the "strength of the non-Hermiticity" is controlled by the two parameters, viz., by an imaginary coupling ig and by the distance d of its onset from the origin. We solve this problem and confirm that the spectrum is discrete and real in a non-empty interval of g. Surprisingly, a specific distinction between the bound states is found in their asymptotic stability/instability with respect to an unlimited growth of g. In our model, all of the low-lying levels remain asymptotically unstable at the small d and finite L while only the stable levels survive for d near L or in the purely imaginary well with infinite L. In between these two extremes, an unusual and tunable, variable pattern of the interspersed "robust" and "fragile" subspectra of the real levels is obtained.
{
"annotation_id": "05d37fbf-1053-4867-858b-e866cad98612",
"date_created": "2026-03-02T18:02:13.557000Z",
"date_modified": "2026-03-02T18:02:13.557000Z",
"file_hash": "8a9d4a058ecc175f1afa340b2dc8590c6a3d9c7ace343faecc7e1f201ccb4e2e",
"private": false,
"record": {
"abstract": "We study the spectrum in such a PT-symmetric square well of a diameter L\nwhere the \"strength of the non-Hermiticity\" is controlled by the two\nparameters, viz., by an imaginary coupling ig and by the distance d of its\nonset from the origin. We solve this problem and confirm that the spectrum is\ndiscrete and real in a non-empty interval of g. Surprisingly, a specific\ndistinction between the bound states is found in their asymptotic\nstability/instability with respect to an unlimited growth of g. In our model,\nall of the low-lying levels remain asymptotically unstable at the small d and\nfinite L while only the stable levels survive for d near L or in the purely\nimaginary well with infinite L. In between these two extremes, an unusual and\ntunable, variable pattern of the interspersed \"robust\" and \"fragile\" subspectra\nof the real levels is obtained.",
"arxiv_id": "quant-ph/0410196",
"authors": [
"Miloslav Znojil"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1925249",
"journal_ref": "J.Math.Phys. 46 (2005) 062109",
"title": "Solvable PT-symmetric model with a tunable interspersion of non-merging levels",
"url": "https://arxiv.org/abs/quant-ph/0410196"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9629e464-eaea-4c48-ac48-1bdf39be59cb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}