dorsal/arxiv
View SchemaAlternative Perspective on Quantum Tunneling and Instantons
| Authors | F. Paradis, H. Kroger, G. Melkonyan, K. J. M. Moriarty |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408051 |
| URL | https://arxiv.org/abs/quant-ph/0408051 |
| DOI | 10.1103/PhysRevA.71.022106 |
| Journal | Phys.Rev. A71 (2005) 022106 |
Abstract
We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of 1e-5. In contrast to the classical potential, the quantum potential has a triple-well if the classical wells are deep enough. Its minima are located at the position of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instatons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semi-classical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such case is illustrated by an example.
{
"annotation_id": "7b6f195f-3c64-4576-8d02-7d964b73657a",
"date_created": "2026-03-02T18:02:10.298000Z",
"date_modified": "2026-03-02T18:02:10.298000Z",
"file_hash": "45bcd12d7635d3dd82a9f65eeb2d63792635686376d64f0bbe57bb555bc5d246",
"private": false,
"record": {
"abstract": "We present a new way to compute and interpret quantum tunneling in a 1-D\ndouble-well potential. For large transition time we show that the quantum\naction functional gives an analytical expression for tunneling amplitudes. This\nhas been confirmed by numerical simulations giving relative errors in the order\nof 1e-5. In contrast to the classical potential, the quantum potential has a\ntriple-well if the classical wells are deep enough. Its minima are located at\nthe position of extrema of the ground state wave function. The striking feature\nis that a single trajectory with a double instanton reproduces the tunneling\namplitude. This is in contrast to the standard instanton approach, where\ninfinitely many instantons and anti-instatons have to be taken into account.\nThe quantum action functional is valid in the deep quantum regime in contrast\nto the semi-classical regime where the standard instanton approach holds. We\ncompare both approaches via numerical simulations. While the standard instanton\npicture describes only the transition between potential minima of equal depth,\nthe quantum action may give rise to instantons also for asymmetric potential\nminima. Such case is illustrated by an example.",
"arxiv_id": "quant-ph/0408051",
"authors": [
"F. Paradis",
"H. Kroger",
"G. Melkonyan",
"K. J. M. Moriarty"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.022106",
"journal_ref": "Phys.Rev. A71 (2005) 022106",
"title": "Alternative Perspective on Quantum Tunneling and Instantons",
"url": "https://arxiv.org/abs/quant-ph/0408051"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1ad0c986-c6c6-489d-b48f-9ac10eb90b0e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}