dorsal/arxiv
View SchemaInconsistencies of the Adiabatic Theorem and the Berry Phase
| Authors | A. K. Pati, A. K. Rajagopal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405129 |
| URL | https://arxiv.org/abs/quant-ph/0405129 |
Abstract
The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that time apart from phase factors. Recently, Marzlin and Sanders have pointed out that this could lead to apparent violation of unitarity. We resolve the Marzlin-Sanders inconsistency within the quantum adiabatic theorem. Yet, our resolution points to another inconsistency, namely, that the cyclic as well as non-cyclic adiabatic Berry phases may vanish under strict adiabatic condition. We resolve this inconsistency and develop an unitary operator decomposition method to argue for the validity of the adiabatic approximation.
{
"annotation_id": "87dbc410-da82-432a-aa95-69d14bdac70f",
"date_created": "2026-03-02T18:02:06.390000Z",
"date_modified": "2026-03-02T18:02:06.390000Z",
"file_hash": "7d91a1bc1363c65c2d0007454c19f4e509749730ccf3545e7797e4e1f55ebc32",
"private": false,
"record": {
"abstract": "The adiabatic theorem states that if we prepare a quantum system in one of\nthe instantaneous eigenstates then the quantum number is an adiabatic invariant\nand the state at a later time is equivalent to the instantaneous eigenstate at\nthat time apart from phase factors. Recently, Marzlin and Sanders have pointed\nout that this could lead to apparent violation of unitarity. We resolve the\nMarzlin-Sanders inconsistency within the quantum adiabatic theorem. Yet, our\nresolution points to another inconsistency, namely, that the cyclic as well as\nnon-cyclic adiabatic Berry phases may vanish under strict adiabatic condition.\nWe resolve this inconsistency and develop an unitary operator decomposition\nmethod to argue for the validity of the adiabatic approximation.",
"arxiv_id": "quant-ph/0405129",
"authors": [
"A. K. Pati",
"A. K. Rajagopal"
],
"categories": [
"quant-ph"
],
"title": "Inconsistencies of the Adiabatic Theorem and the Berry Phase",
"url": "https://arxiv.org/abs/quant-ph/0405129"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b69f36e4-e1f7-4abb-b9a0-eff27dfb67b5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}