Abstract
The internal intersite motions of the self-trapped carriers of large (bi)polarons locally soften the vibrational modes to which they are coupled. Distinctively, this effect only occurs for phonon half wavelengths that are shorter than the diameter of the self-trapped carrier. With sufficiently strong electron-lattice coupling, distinct extra lower-frequency near replicas of the short-wavelength portion of the vibrational modes result. This unusual effect is consistent with observations in high-${\mathit{T}}_{\mathit{c}}$ superconductors.
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