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 Z<sup>v</sup>. We proved the essen...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 Z<sup>v</sup>. 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.展开更多
Introduction Chirality is defined as the absence of inversion symmetry,however,it is actually a pseudo-scalar of objects or figures,and does not depend for its definition on any connection to the physical world[1-5]. ...Introduction Chirality is defined as the absence of inversion symmetry,however,it is actually a pseudo-scalar of objects or figures,and does not depend for its definition on any connection to the physical world[1-5]. Logically,chiral molecules may possess other inherent physical quantity that guarantees the connection to the physical world[6,7].展开更多
Multiconfiguration quantum chemical calculation of geometry and electron properties of Fe2Si18 cluster indicates on the predictable change of spin states as a function of the excitation energy beginning from ground st...Multiconfiguration quantum chemical calculation of geometry and electron properties of Fe2Si18 cluster indicates on the predictable change of spin states as a function of the excitation energy beginning from ground state with the total spin S = 4. The charges on the two Fe atoms are quite different as well as the charge distribution on the surrounding Si atoms. Nevertheless the total dipole moment of the cluster is a monotonically decreasing function of the excitation energy and it reaches practically zero value in the first singlet state in which the cluster represents a new version of a quibit system.展开更多
文摘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 Z<sup>v</sup>. 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.
基金Supported by the National Natural Science Foundation of China(No.60171008)Shanghai Science and Technology Commit-tee(No.0452nm087).
文摘Introduction Chirality is defined as the absence of inversion symmetry,however,it is actually a pseudo-scalar of objects or figures,and does not depend for its definition on any connection to the physical world[1-5]. Logically,chiral molecules may possess other inherent physical quantity that guarantees the connection to the physical world[6,7].
文摘Multiconfiguration quantum chemical calculation of geometry and electron properties of Fe2Si18 cluster indicates on the predictable change of spin states as a function of the excitation energy beginning from ground state with the total spin S = 4. The charges on the two Fe atoms are quite different as well as the charge distribution on the surrounding Si atoms. Nevertheless the total dipole moment of the cluster is a monotonically decreasing function of the excitation energy and it reaches practically zero value in the first singlet state in which the cluster represents a new version of a quibit system.
