# Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory

## Abstract

Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.

- Authors:

- V. Fock Institute of Physics, St Petersburg State University, St Petersburg 198504, (Russian Federation)
- (Sweden)

- Publication Date:

- OSTI Identifier:
- 20982064

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022105; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LANDAU-ZENER FORMULA; LIFETIME; PERTURBATION THEORY; POTENTIAL ENERGY; PROBABILITY; SURFACES

### Citation Formats

```
Volkov, M. V., Department of Physics, AlbaNova University Center, Stockholm University, 106 91 Stockholm, and Ostrovsky, V. N.
```*Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022105.

```
Volkov, M. V., Department of Physics, AlbaNova University Center, Stockholm University, 106 91 Stockholm, & Ostrovsky, V. N.
```*Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory*. United States. doi:10.1103/PHYSREVA.75.022105.

```
Volkov, M. V., Department of Physics, AlbaNova University Center, Stockholm University, 106 91 Stockholm, and Ostrovsky, V. N. Thu .
"Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory". United States.
doi:10.1103/PHYSREVA.75.022105.
```

```
@article{osti_20982064,
```

title = {Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory},

author = {Volkov, M. V. and Department of Physics, AlbaNova University Center, Stockholm University, 106 91 Stockholm and Ostrovsky, V. N.},

abstractNote = {Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.},

doi = {10.1103/PHYSREVA.75.022105},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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