dorsal/arxiv
View SchemaSpectral singularities of non-Hermitian Hamiltonians and SUSY transformations
| Authors | Boris F Samsonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507085 |
| URL | https://arxiv.org/abs/quant-ph/0507085 |
| DOI | 10.1088/0305-4470/38/34/L02 |
| Journal | J. Phys. A: Math. Gen. 38 (2005) L571-L579 |
Abstract
Simple examples of non-Hermitian Hamiltonians with purely real spectra defined in $L^2(R^+)$ having spectral singularities inside the continuous spectrum are given. It is shown that such Hamiltonians may appear by shifting the ndependent variable of a real potential into the complex plane. Also they may be created as SUSY partners of Hermitian Hamiltonians. In the latter case spectral singularities of a non-Hermitian Hamiltonian are ordinary points of the continuous spectrum for its Hermitian SUSY partner. Conditions for transformation functions are formulated when a complex potential with complex eigenenergies and spectral singularities has a SUSY partner with a real spectrum without spectral singularities. Finally we shortly discuss why Hamiltonians with spectral singularities are `bad'.
{
"annotation_id": "83cf0e2d-2c86-42ae-bd2c-7f05f2d0601a",
"date_created": "2026-03-02T18:02:17.048000Z",
"date_modified": "2026-03-02T18:02:17.048000Z",
"file_hash": "c58a5dfc66792a6cfe918b1510319bd7d3099a19342e50c612b393b9ba449490",
"private": false,
"record": {
"abstract": "Simple examples of non-Hermitian Hamiltonians with purely real spectra\ndefined in $L^2(R^+)$ having spectral singularities inside the continuous\nspectrum are given. It is shown that such Hamiltonians may appear by shifting\nthe ndependent variable of a real potential into the complex plane. Also they\nmay be created as SUSY partners of Hermitian Hamiltonians. In the latter case\nspectral singularities of a non-Hermitian Hamiltonian are ordinary points of\nthe continuous spectrum for its Hermitian SUSY partner. Conditions for\ntransformation functions are formulated when a complex potential with complex\neigenenergies and spectral singularities has a SUSY partner with a real\nspectrum without spectral singularities. Finally we shortly discuss why\nHamiltonians with spectral singularities are `bad\u0027.",
"arxiv_id": "quant-ph/0507085",
"authors": [
"Boris F Samsonov"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/34/L02",
"journal_ref": "J. Phys. A: Math. Gen. 38 (2005) L571-L579",
"title": "Spectral singularities of non-Hermitian Hamiltonians and SUSY transformations",
"url": "https://arxiv.org/abs/quant-ph/0507085"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "acfae6f9-4c92-47bc-a04d-a5d0dfa2e4a6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}