dorsal/arxiv
View SchemaA new perturbative approach to the adiabatic approximation
| Authors | R. MacKenzie, E. Marcotte, H. Paquette |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510024 |
| URL | https://arxiv.org/abs/quant-ph/0510024 |
| DOI | 10.1103/PhysRevA.73.042104 |
| Journal | Phys. Rev. A 73, 042104 (2006) |
Abstract
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous eigenstate of the initial Hamiltonian is written as a power series which has a straightforward diagrammatic representation. Each term of the series corresponds to a sequence of "adiabatic" evolutions, during which the system remains in an instantaneous eigenstate of the Hamiltonian, punctuated by transitions from one state to another. The first term of this series is the standard adiabatic evolution, the next is the well-known first correction to it, and subsequent terms can be written down essentially by inspection. Although the final result is perhaps not terribly surprising, it seems to be not widely known, and the interpretation is new, as far as we know. Application of the method to the adiabatic approximation is given, and some discussion of the validity of this approximation is presented.
{
"annotation_id": "d7a887bb-3e1b-419e-b7ae-0973e453a2e9",
"date_created": "2026-03-02T18:02:19.686000Z",
"date_modified": "2026-03-02T18:02:19.686000Z",
"file_hash": "8fc9b835816a23d8942f04958efe3884149a25d1bb7bcb0c2fb55b63d9cdd01f",
"private": false,
"record": {
"abstract": "A new and intuitive perturbative approach to time-dependent quantum mechanics\nproblems is presented, which is useful in situations where the evolution of the\nHamiltonian is slow. The state of a system which starts in an instantaneous\neigenstate of the initial Hamiltonian is written as a power series which has a\nstraightforward diagrammatic representation. Each term of the series\ncorresponds to a sequence of \"adiabatic\" evolutions, during which the system\nremains in an instantaneous eigenstate of the Hamiltonian, punctuated by\ntransitions from one state to another. The first term of this series is the\nstandard adiabatic evolution, the next is the well-known first correction to\nit, and subsequent terms can be written down essentially by inspection.\nAlthough the final result is perhaps not terribly surprising, it seems to be\nnot widely known, and the interpretation is new, as far as we know. Application\nof the method to the adiabatic approximation is given, and some discussion of\nthe validity of this approximation is presented.",
"arxiv_id": "quant-ph/0510024",
"authors": [
"R. MacKenzie",
"E. Marcotte",
"H. Paquette"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.042104",
"journal_ref": "Phys. Rev. A 73, 042104 (2006)",
"title": "A new perturbative approach to the adiabatic approximation",
"url": "https://arxiv.org/abs/quant-ph/0510024"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9d86a07d-b8b2-429f-8914-fbc42a32d613",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}