dorsal/arxiv
View SchemaTemporal behavior of quantum mechanical systems
| Authors | Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9509016 |
| URL | https://arxiv.org/abs/quant-ph/9509016 |
| DOI | 10.1142/S0217979296000118 |
Abstract
The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system. Some attempts at extracting the exponential decay law from quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known ``$\lambda^2T$" limit. We clarify these general arguments by introducing and studying a solvable dynamical model. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.
{
"annotation_id": "b4514c8f-a5eb-49d9-9e6c-85d603e987a1",
"date_created": "2026-03-02T18:02:37.343000Z",
"date_modified": "2026-03-02T18:02:37.343000Z",
"file_hash": "dcf856508988a50eac5677d0d17b0301810cf678e2f24009f9fbc3dd4e0cf9c5",
"private": false,
"record": {
"abstract": "The temporal behavior of quantum mechanical systems is reviewed. We study the\nso-called quantum Zeno effect, that arises from the quadratic short-time\nbehavior, and the analytic properties of the ``survival\" amplitude. It is shown\nthat the exponential behavior is due to the presence of a simple pole in the\nsecond Riemannian sheet, while the contribution of the branch point yields a\npower behavior for the amplitude. The exponential decay form is cancelled at\nshort times and dominated at very long times by the branch-point contributions,\nwhich give a Gaussian behavior for the former and a power behavior for the\nlatter. In order to realize the exponential law in quantum theory, it is\nessential to take into account a certain kind of macroscopic nature of the\ntotal system. Some attempts at extracting the exponential decay law from\nquantum theory, aiming at the master equation, are briefly reviewed, including\nvan Hove\u0027s pioneering work and his well-known ``$\\lambda^2T$\" limit. We clarify\nthese general arguments by introducing and studying a solvable dynamical model.\nSome implications for the quantum measurement problem are also discussed, in\nparticular in connection with dissipation.",
"arxiv_id": "quant-ph/9509016",
"authors": [
"Hiromichi Nakazato",
"Mikio Namiki",
"Saverio Pascazio"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1142/S0217979296000118",
"title": "Temporal behavior of quantum mechanical systems",
"url": "https://arxiv.org/abs/quant-ph/9509016"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f70f358e-0ef7-4a85-af57-cd5b65a2e917",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}