dorsal/arxiv
View SchemaPhase rigidity and avoided level crossings in the complex energy plane
| Authors | E. N. Bulgakov, I. Rotter, A. F. Sadreev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605056 |
| URL | https://arxiv.org/abs/quant-ph/0605056 |
| DOI | 10.1103/PhysRevE.74.056204 |
Abstract
We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $\phi_\lambda$ and define the value $r_\lambda = (\phi_\lambda|\phi_\lambda)/<\phi_\lambda|\phi_\lambda>$ that characterizes the phase rigidity of the eigenfunctions $\phi_\lambda$. In the scenario with avoided level crossings, $r_\lambda$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_\lambda$ may be considered as an internal property of an {\it open} quantum system. In the literature, the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ is considered. Since $\Psi^E_C$ can be represented in the interior of the system by the $\phi_\lambda$, the phase rigidity $\rho$ of the $\Psi^E_C$ is related to the $r_\lambda$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $\rho$ to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant with respect to the effective Hamiltonian. We illustrate the relation between phase rigidity $\rho$ and transmission numerically for small open cavities.
{
"annotation_id": "a72e218f-e478-4b19-a34b-49e9d5cb78a0",
"date_created": "2026-03-02T18:02:27.677000Z",
"date_modified": "2026-03-02T18:02:27.677000Z",
"file_hash": "c8cc570e27f98cdf4a0be66e2c6724f7eb73ed76b82273793462ec9570c5ef21",
"private": false,
"record": {
"abstract": "We consider the effective Hamiltonian of an open quantum system, its\nbiorthogonal eigenfunctions $\\phi_\\lambda$ and define the value $r_\\lambda =\n(\\phi_\\lambda|\\phi_\\lambda)/\u003c\\phi_\\lambda|\\phi_\\lambda\u003e$ that characterizes the\nphase rigidity of the eigenfunctions $\\phi_\\lambda$. In the scenario with\navoided level crossings, $r_\\lambda$ varies between 1 and 0 due to the mutual\ninfluence of neighboring resonances. The variation of $r_\\lambda$ may be\nconsidered as an internal property of an {\\it open} quantum system. In the\nliterature, the phase rigidity $\\rho$ of the scattering wave function\n$\\Psi^E_C$ is considered. Since $\\Psi^E_C$ can be represented in the interior\nof the system by the $\\phi_\\lambda$, the phase rigidity $\\rho$ of the\n$\\Psi^E_C$ is related to the $r_\\lambda$ and therefore also to the mutual\ninfluence of neighboring resonances. As a consequence, the reduction of the\nphase rigidity $\\rho$ to values smaller than 1 should be considered, at least\npartly, as an internal property of an open quantum system in the overlapping\nregime. The relation to measurable values such as the transmission through a\nquantum dot, follows from the fact that the transmission is, in any case,\nresonant with respect to the effective Hamiltonian. We illustrate the relation\nbetween phase rigidity $\\rho$ and transmission numerically for small open\ncavities.",
"arxiv_id": "quant-ph/0605056",
"authors": [
"E. N. Bulgakov",
"I. Rotter",
"A. F. Sadreev"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.74.056204",
"title": "Phase rigidity and avoided level crossings in the complex energy plane",
"url": "https://arxiv.org/abs/quant-ph/0605056"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4c54ef1e-a6cf-419b-85f9-00d05eb68e34",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}