DOI: 10.1063/1.473364. Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case

Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case

10.1063/1.473364

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A two-by-two diabatic propagation method is developed to deal with general one-dimensional multi-channel curve crossing problems. Each crossing is treated within the newly completed two-state semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (I-matrix). A product of all the I-matrices yields the reduced scattering matrix for the entire system. This theory can handle the multi-channel curve crossing problems as simply as a two-state problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a seven-state system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the state-to-state transitions are well reproduced by the present semiclassical theory.

Bibliography

Zhu, C., & Nakamura, H. (1997). Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case. The Journal of Chemical Physics, 106(7), 2599â2611.

Authors 2

Chaoyuan Zhu (first)
Hiroki Nakamura (additional)

References 18 Referenced 63

10.1063/1.469057 / J. Chem. Phys. (1995)
10.1063/1.467877 / J. Chem. Phys. (1994)
{'key': '2024020620434212400_r3', 'first-page': '249', 'volume': '32', 'year': '1996', 'journal-title': 'Comments At. Mol. Phys.'} / Comments At. Mol. Phys. (1996)
{'key': '2024020620434212400_r4'}
10.1080/00018737100101281 / Adv. Phys. (1971)
{'key': '2024020620434212400_r6'}
10.1080/01442359109353256 / Int. Rev. Phys. Chem. (1991)
{'key': '2024020620434212400_r8'}
{'key': '2024020620434212400_r9', 'first-page': '46', 'volume': '2', 'year': '1932', 'journal-title': 'Phys. Z. Sowjetunion'} / Phys. Z. Sowjetunion (1932)
{'key': '2024020620434212400_r10', 'first-page': '696', 'volume': 'AB7', 'year': '1932', 'journal-title': 'Proc. R. Soc. Ser.'} / Proc. R. Soc. Ser. (1932)
{'key': '2024020620434212400_r11', 'first-page': '369', 'volume': '5', 'year': '1932', 'journal-title': 'Helv. Phys. Acta'} / Helv. Phys. Acta (1932)
{'key': '2024020620434212400_r12'}
10.1063/1.452907 / J. Chem. Phys. (1987)
{'key': '2024020620434212400_r14', 'first-page': '916', 'volume': '26', 'year': '1968', 'journal-title': 'Sov. Phys. JETP'} / Sov. Phys. JETP (1968)
10.1039/DC9735500030 / Faraday Discuss. Chem. Soc. (1973)
{'key': '2024020620434212400_r16', 'first-page': '51', 'volume': '20', 'year': '1980', 'journal-title': 'Mol. Phys.'} / Mol. Phys. (1980)
10.1016/0009-2614(96)00661-6 / Chem. Phys. Lett. (1996)
10.1103/PhysRevA.25.3399 / Phys. Rev. A (1982)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:15 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 7:24 p.m.)
Indexed	4 days ago (Aug. 28, 2025, 8:43 a.m.)
Issued	28 years, 6 months ago (Feb. 15, 1997)
Published	28 years, 6 months ago (Feb. 15, 1997)
Published Print	28 years, 6 months ago (Feb. 15, 1997)

Funders 0

None

BibTeX

@article{Zhu_1997, title={Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case}, volume={106}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.473364}, DOI={10.1063/1.473364}, number={7}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Zhu, Chaoyuan and Nakamura, Hiroki}, year={1997}, month=feb, pages={2599–2611} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        28
      ]
    ],
    "date-time": "2025-08-28T12:43:29Z",
    "timestamp": 1756385009293
  },
  "reference-count": 18,
  "publisher": "AIP Publishing",
  "issue": "7",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1997,
        2,
        15
      ]
    ]
  },
  "abstract": "<jats:p>A two-by-two diabatic propagation method is developed to deal with general one-dimensional multi-channel curve crossing problems. Each crossing is treated within the newly completed two-state semiclassical theory in the diabatic representation and is represented by a nonadiabatic transition matrix (I-matrix). A product of all the I-matrices yields the reduced scattering matrix for the entire system. This theory can handle the multi-channel curve crossing problems as simply as a two-state problem. An analysis of the complex crossing points in the momentum space can provide a comprehensive illustrative criterion of this method. A detailed severe numerical test is made by taking a seven-state system with 6 and 12 nonzero diabatic couplings. It is demonstrated that dominant processes among the state-to-state transitions are well reproduced by the present semiclassical theory.</jats:p>",
  "DOI": "10.1063/1.473364",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:15:29Z",
    "timestamp": 1027685729000
  },
  "page": "2599-2611",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 63,
  "title": "Semiclassical theory of multi-channel curve crossing problems: Landau-Zener case",
  "prefix": "10.1063",
  "volume": "106",
  "author": [
    {
      "given": "Chaoyuan",
      "family": "Zhu",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Division of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444, Japan"
        }
      ]
    },
    {
      "given": "Hiroki",
      "family": "Nakamura",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Division of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444, Japan"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020620434212400_r1",
      "doi-asserted-by": "crossref",
      "first-page": "7448",
      "DOI": "10.1063/1.469057",
      "volume": "102",
      "year": "1995",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020620434212400_r2",
      "doi-asserted-by": "crossref",
      "first-page": "10630",
      "DOI": "10.1063/1.467877",
      "volume": "101",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020620434212400_r3",
      "first-page": "249",
      "volume": "32",
      "year": "1996",
      "journal-title": "Comments At. Mol. Phys."
    },
    {
      "key": "2024020620434212400_r4"
    },
    {
      "key": "2024020620434212400_r5",
      "doi-asserted-by": "crossref",
      "first-page": "405",
      "DOI": "10.1080/00018737100101281",
      "volume": "20",
      "year": "1971",
      "journal-title": "Adv. Phys."
    },
    {
      "key": "2024020620434212400_r6"
    },
    {
      "key": "2024020620434212400_r7",
      "doi-asserted-by": "crossref",
      "first-page": "123",
      "DOI": "10.1080/01442359109353256",
      "volume": "10",
      "year": "1991",
      "journal-title": "Int. Rev. Phys. Chem."
    },
    {
      "key": "2024020620434212400_r8"
    },
    {
      "key": "2024020620434212400_r9",
      "first-page": "46",
      "volume": "2",
      "year": "1932",
      "journal-title": "Phys. Z. Sowjetunion"
    },
    {
      "key": "2024020620434212400_r10",
      "first-page": "696",
      "volume": "AB7",
      "year": "1932",
      "journal-title": "Proc. R. Soc. Ser."
    },
    {
      "key": "2024020620434212400_r11",
      "first-page": "369",
      "volume": "5",
      "year": "1932",
      "journal-title": "Helv. Phys. Acta"
    },
    {
      "key": "2024020620434212400_r12"
    },
    {
      "key": "2024020620434212400_r13",
      "doi-asserted-by": "crossref",
      "first-page": "4031",
      "DOI": "10.1063/1.452907",
      "volume": "87",
      "year": "1987",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020620434212400_r14",
      "first-page": "916",
      "volume": "26",
      "year": "1968",
      "journal-title": "Sov. Phys. JETP"
    },
    {
      "key": "2024020620434212400_r15",
      "doi-asserted-by": "crossref",
      "first-page": "30",
      "DOI": "10.1039/DC9735500030",
      "volume": "55",
      "year": "1973",
      "journal-title": "Faraday Discuss. Chem. Soc."
    },
    {
      "key": "2024020620434212400_r16",
      "first-page": "51",
      "volume": "20",
      "year": "1980",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020620434212400_r17",
      "doi-asserted-by": "crossref",
      "first-page": "342",
      "DOI": "10.1016/0009-2614(96)00661-6",
      "volume": "258",
      "year": "1996",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020620434212400_r18",
      "doi-asserted-by": "crossref",
      "first-page": "3399",
      "DOI": "10.1103/PhysRevA.25.3399",
      "volume": "25",
      "year": "1982",
      "journal-title": "Phys. Rev. A"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/106/7/2599/19247555/2599_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/106/7/2599/19247555/2599_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T00:24:59Z",
    "timestamp": 1707265499000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/106/7/2599/476411/Semiclassical-theory-of-multi-channel-curve"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1997,
        2,
        15
      ]
    ]
  },
  "references-count": 18,
  "journal-issue": {
    "issue": "7",
    "published-print": {
      "date-parts": [
        [
          1997,
          2,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.473364",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1997,
        2,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1997,
        2,
        15
      ]
    ]
  }
}