FROM WEAK TO STRONG-COUPLING SUPERCONDUCTIVITY - COLLECTIVE MODES IN A MODEL WITH LOCAL ATTRACTION

We discuss the density-density response functions and the collective e xcitation spectrum for the extended Hubbard model with on-site attract ion and arbitrary electron density, in the superconducting ground stat e. For the short-range intersite interaction we find the sound wave-li ke modes with the velocity interpolating smoothly between the weak (v is-proportional-to 2Zt, Absolute value of U much less than 2Zt) and st rong coupling (v is-proportional-to Zt2/Absolute value of U, Absolute value of U much greater than 2Zt) limits. The latter agrees with the r esults obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit. In the weak coupling regime, we obtain that apa rt from a commensurate charge density wave instability, an increase in the intersite Coulomb repulsion can give rise to a charge density wav e incommensurate with the lattice period, away from half-filling. The ground state phase diagram for 2D square lattice, including singlet su perconducting ground state, electronic droplet formation, and charge d ensity waves is determined. It is also shown that the energy of collec tive excitations evolves smoothly from weak to strong coupling limit f or a 2D lattice, in the case of a long-range Coulomb interaction. Fina lly, the mode coupling effects in the frequency behavior of the densit y-density response functions are analyzed.