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Spectra of the Energy Operator of Four-Electron Systems in the Impurity Hubbard Model. Triplet state

Journal of Applied Mathematics and Physics 2021年第11期9卷 2776-2795页

作者： S. M. Tashpulatov R. T. Parmanova Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

关键词： Hubbard Model Essential Spectrum Discrete Spectrum Four Electron Systems quintet state Triplet state Singlet state Spectra

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Four-Electron Systems in the Impurity Hubbard Model. Second Triplet state. Spectra of the System in the ν-Dimensional Lattice Z^ν

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Journal of Applied Mathematics and Physics 2023年第11期11卷 3393-3427页

作者： S. M. Tashpulatov R. T. Parmanova Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider an energy operator of four-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. The spectrum of the systems in the second triplet state in a ν-dimensional lattice is investigated. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model for the second triplet state of the system. The investigations show that the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

关键词： Spectra of Four-Electron System Bound state Anti-Bound state Impurity Hubbard Model quintet state Singlet state Triplet state

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Structure of Essential Spectra and Discrete Spectrum of the Energy Operator of Six-Electron Systems in the Hubbard Model. First quintet and First Singlet states

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Journal of Applied Mathematics and Physics 2022年第11期10卷 3424-3461页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the ... 详细信息

关键词： Hubbard Model Essential Spectrum Discrete Spectrum Six Electron Systems Octet state Singlet state quintet state

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