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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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Spectra of the Energy Operator of Two-Electron System in the impurity hubbard model

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Journal of Applied Mathematics and Physics 2022年第9期10卷 2743-2779页

作者： Sa’dulla Tashpulatov Laboratory Physics of Multiparticle Systems Institute of Nuclear Physics of the Academy of Sciences of the Republic of Uzbekistan Tashkent Uzbekistan

We consider two-electron systems for the impurity hubbard model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Zv. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-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 two-electron systems in an impurity hubbard model.

关键词： Two-Electron System impurity hubbard model Singlet State Triplet State Essential Spectra Discrete Spectrum

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The Structure of Essential Spectra and Discrete Spectrum of Three-Electron Systems in the impurity hubbard model—Quartet State

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Journal of Applied Mathematics and Physics 2021年第6期9卷 1391-1421页

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

We consider a three-electron system in the impurity hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity hubbard model in the quartet state of the system in a v-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the impurity hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.

关键词： Essential Spectrum Discrete Spectrum Three-Electron System Local impurity States impurity hubbard model Quartet State Doublet State

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