In the Holstein model, the superconducting collective mode frequency evolves from about 2Δ_P in the BCS regime to the soft phonon in the crossover and to the superfluid stiffness in the BEC regime, with weight proportional to the pairing gap.
Importance of phase fluctuations in superconductors with small superfluid density,
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Collective mode across the BCS-BEC crossover in Holstein model
In the Holstein model, the superconducting collective mode frequency evolves from about 2Δ_P in the BCS regime to the soft phonon in the crossover and to the superfluid stiffness in the BEC regime, with weight proportional to the pairing gap.