By inserting quasielectron energies $\ensuremath{\omega}$ calculated from the fully renormalized Green's function of the Hubbard model obtained in the preceding paper into the exact expression of Galitskii and Migdal, the ground-state energy, the chemical potential, and the dynamic- and thermodynamic-stability conditions are calculated in the narrow-band region. The results show that as long as the interaction energy
I is finite, electrons in the narrow-band region do not obey the Landau theory of Fermi liquids, and a gap appears between the lowest quasielectron energy $\ensuremath{\omega}$ and the chemical potential $\ensuremath{\mu}$ for any occupation
n, regardless of whether the lower band is exactly filled or not. This unusual behavior is possible because, when an electron is added to the system of
N electrons, the whole system relaxes due to the strong interaction, introducing a relaxation energy difference between the two quantities. We also show that all previous solutions which exhibit the split-band structure, including Hubbard's work, yield the same conclusion that electrons do not behave like Landau quasiparticles. However, the energy gap is calculated to be negative at least for some occupations
n, demonstrating the dynamic instability of those solutions. They also exhibit thermodynamic instability for certain occupations, while the fully renormalized solution, having sufficient electron correlations built in, satisfies the dynamic and thermodynamic stability conditions for all occupations. When the lower band is nearly filled, the nature of the solution is shown to change, making the coherent motion of electrons with fixed
k values more difficult. In the pathological limit where $I=\ensuremath{\infty}$, however, the gap vanishes, yielding a metallic state.
Two-band models (one wide band and one narrow band close to the Fermi energy) and local-pair models (periodic Anderson model) of high- T c superconductors give rise to the same equilibrium thermodynamics despite the different physical pictures underlying the models. The low-energy excitations in these models are, however, not of the same character, which leads to a qualitative difference in their non-equilibrium properties. In particular, this is true for the interband optical absorption at threshold. Using the Golden rule for absorption and a mean-field treatment of the superconducting state, we calculate the threshold absorption at zero temperature for three different cases: a two-band model without additional correlation besides the interband interaction between Cooper pairs; a two-band model with attractive correlation (negative- U ) between electrons on the same site in the narrow band; and a local-pair model with the same correlation as in the previous model, but with a pair interaction due to the hybridization (in second order) of the wide band and the local states. In the two latter models (which are closely related), we assume that the local-pair correlation energy is much higher than T c . In the uncorrelated case the absorption has a square-root singularity at threshold, which is due to the diverging density of states of the one-particle excitations. In the negative- U correlated cases no single-particle transitions are possible at threshold, and only direct two-photon two-particle processes are possible. Further, in the local-pair model the hybridization can act together with a photon, giving an additional one-photon two-electron threshold in the absorption.