Structure of the essential spectrum and the discrete spectrum of the energy operator of three-magnon systems in the Heisenberg model
- Authors: Tashpulatov S.M.1
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Affiliations:
- Institute of Nuclear Physics, Academy of Sciences of Uzbekistan
- Issue: Vol 242 (2025)
- Pages: 82-91
- Section: Articles
- URL: https://medbiosci.ru/2782-4438/article/view/312574
- DOI: https://doi.org/10.36535/2782-4438-2025-242-82-91
- ID: 312574
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Abstract
We consider the energy operator of three-magnon systems in the Heisenberg model and examine the structure of the essential spectrum and the discrete spectrum of the system in the $\nu$-dimensional lattice $Z^{\nu}$ with the coupling nearest neighbors.
About the authors
Sadulla Mamarazhabovich Tashpulatov
Institute of Nuclear Physics, Academy of Sciences of Uzbekistan
Author for correspondence.
Email: toshpul@mail.ru
Doctor of physico-mathematical sciences, Senior Researcher
References
- Гочев И. Г., “Двухмагнонные состояния в одномерной модели Гейзенберга с взаимодействием вторых соседей”, Теор. мат. физ., 15 (1973), 402–406
- Гочев И. Г., “Связанные состояния магнонов в линейной анизотропной цепочке.”, ЖЭТФ., 61:10 (1971), 1674–1678
- Наймарк М. А., Нормированные кольца, Наука, М., 1968
- Ташпулатов С. М., “Исследование спектра оператора энергии двухмагнонной системы в одномерном анизотропном ферромагнетике Гейзенберга с взаимодействием вторых соседей”, Теор. мат. физ., 107:1 (1996), 155–161
- Bethe H. A., “Eigenverte und Eigenfunction der linearen Atom kette”, Z. Phys., 71 (1931), 205–226
- Fukuda N., Wortis M., “Bound states in the spin wave problem”, Phys. Chem. Solids., 24 (1963), 1675–1677
- Ichinose T., “Spectral properties of tensor products of linear operators, 1”, Trans. Am. Math. Soc., 235 (1978), 75–113
- Ichinose T., “Spectral properties of tensor products of linear operators, 2. The approximate point spectrum and Kato essential spectrum”, Trans. Am. Math. Soc., 237 (1978), 223–254
- Ichinose T., “Tensor products of linear operators. Spectral theory”, Banach Center Publ., 8 (1982), 294–300
- Majumdar C. K., “Bound states of two spin waves in the Heisenberg ferromagnet with nearest and next nearest neighbours interactions”, J. Math. Phys., 132 (1969), 85
- Ono I., Mikado I. S., Oguchi T., “Two-magnon bound states in a linear Heisenberg chain with nearest and next nearest neighbours interactions”, J. Phys. Soc. Jpn., 30 (1971), 358–366
- Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. 1. Functional Analysis, Academic Press, 1972
- Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. 4. Operator Analysis, Academic Press, New York, 1982
- Tashpulatov S. M., “Structure of essential spectrum and discrete spectrum of the energy operator of three-magnon systems in the isotropic ferromagnetic non-Heisenberg model with spin one and nearest-neighbor interactions”, J. Appl. Math. Phys., 7:4 (2019), 874–899
- Van Himbergen J. E., Tjon J. A., “Three-magnon bound states in the two-dimensional isotropic and anisotropic Heisenberg ferromagnet”, Phys. A., 82 (1976.), 389–416
- Wortis M., “Bound states of two spin waves in the Heisenberg ferromagnet”, Phys. Rev., 132 (1963), 85–97
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