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 ν -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.
Using a new path-integral theory [1], we study the angle resolved photoemission spectra (ARPES) of one - and two-dimensional metallic many-electron systems coupled with Einstein phonons. The multiple scatterings of electrons due to phonons are shown to completely dominate the ARPES, even if the electron-phonon coupling strength is intermediate. These multiple scatterings result in spectral evolution from a broad Gaussian to a two-headed asymmetric Lorentzian as the momentum changes from the band bottom to the Fermi one ( ≡ pF ), as shown in Fig. 1. We have also found that this two-headed structure near pF becomes most distinct in the two dimensional non-half-filled cases with no charge density wave gap. These results qualitatively agree with recent experiments of ARPES on the Be(0001) surface and Bi2Sr2CaCu2O8. In terms of nonlinear couplings between the electrons and the phonons, we also show the microscopic origin of anomalous isotopic band shift appeared in the ARPES of Bi2Sr2CaCu2O8, in good agreement with the recently discovery by Gweon et al. [2].