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Motivated by the short coherence length of the high-temperature superconductors, we study in the negative-U Hubbard model the crossover from Cooper pairs for U{}t to composite bosons for U{}t. We compute the collective-mode spectrum using a generalized random-phase-approximation analysis within the equations-of-motion formalism. We find a smooth evolution of the Anderson mode for weak coupling into the Bogoliubov sound mode for hard-core bosons.
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Belkhir et al. (1992) studied this question.
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