One-dimensional models have been instrumental in enhancing our understanding of the vibrational and electronic properties of crystalline as well as aperiodic structures. Here, we show that the classical motion of a one-dimensional chain of atoms coupled through a specific force function that depends on position shows features very similar to the Wannier-Stark problem of a quantum particle under the combined effects of a periodic lattice potential and a constant electric field. Both problems exhibit localized modes and a ladder of equally spaced eigenfrequencies, leading to temporal dynamics characterized by periodic oscillations. These findings apply broadly to a variety of synthetic systems including acoustic metamaterials and functionally graded composites.
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