CROSSOVER FROM COOPER PAIRS TO COMPOSITE BOSONS - A GENERALIZED RPA ANALYSIS OF COLLECTIVE EXCITATIONS

We study the evolution of the ground state and the excitation spectrum of the two- and three-dimensional attractive (negative-U) Hubbard mod el as the system evolves from a Cooper-pair regime for U << t, to a co mposite-boson regime for U >> t. Our work is motivated by the observat ion that the high-temperature superconductors, with their short cohere nce lengths and unusual normal-state properties, may be in an intermed iate-coupling regime between these two limits. A mean-field analysis o f pairing, suitably generalized to account for a shift in the chemical potential, is known to be able to describe the ground-state crossover as a function of U/t. We compute the collective-mode spectrum using a general random-phase-approximation analysis within the equations-of-m otion formalism. We find a smooth evolution of the Anderson mode for w eak coupling into the Bogoliubov sound mode for hard-core bosons. We t hen include a long-range Coulomb interaction and show that it leads to a plasmon which again evolves smoothly from weak to strong coupling.