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Structure of Essential Spectrum and Discrete Spectra of the Energy Operator of Five-Electron Systems in the Hubbard Model. Third and Fourth doublet states

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Journal of Applied Mathematics and Physics 2020年第12期8卷 2886-2918页

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

We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a v-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.

关键词： Essential Spectrum Discrete Spectrum Five-Electron System Bound state Anti-Bound state Hubbard Model doublet state Sextet state Quartet state

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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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