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 disorde r appears as dimer-type "defects" on appropriately decimated lattices descr ibing the phonon modes of the system. As a consequence of the special reson ance condition where the reflected waves from two sites Of the dimer underg o destructive interference, the decimated lattices exhibit Bloch-type phono n modes for energies that can be tuned by varying the nonlinearity paramete r of the system. In a generalized two-parameter model, where the strength a nd the smoothness of the potential can be controlled independently, our stu dy provides strong evidence of localization in a discrete quasiperiodic pot ential with an infinite number of steps. This localization boundary interwi nes with the parameter region exhibiting the Bloch-type states. [S0163-1829 (99)12113-1].