Lattice vibration in homogeneously-mixed-valent systems of rare-earth materials

We investigate the essential feature of interplay between lattice vibration and valence fluctuation in the homogeneously-mixed-valent systems of rare-earth materials rigorously within simple models, paying special attention to studying the collective nature of excitations in lattice vibration as well as in valence fluctuation. We compare our results with experiments and find that the general features of the experiments of ${\mathrm{Sm}}_{0.75}$ ${\mathrm{Y}}_{0.25}$S are well understood within the present model if we assume the characteristic energy of the valence fluctuation to be comparable to the phonon energy.