Correlated disorder and propagating modes in the frenkel-kontorova model

The incommensurate Frenkel-Kontorova model in its pinned phase is shown to be equivalent to a system with correlated disorder. This correlated disorder appears as dimer-type “defects” on appropriately decimated lattices describing the phonon modes of the system. As a consequence of the special resonance condition where the reflected waves from two sites of the dimer undergo destructive interference, the decimated lattices exhibit Bloch-type phonon modes for energies that can be tuned by varying the nonlinearity parameter of the system. In a generalized two-parameter model, where the strength and the smoothness of the potential can be controlled independently, our study provides strong evidence of localization in a discrete quasiperiodic potential with an infinite number of steps. This localization boundary interwines with the parameter region exhibiting the Bloch-type states.