DYNAMICS OF LATTICE-VIBRATIONS FOR ONE-DIMENSIONAL COMMENSURATE AND INCOMMENSURATE COMPOSITES WITH HARMONIC INTERACTION

We introduce a model that generalizes the. Frenkel-Kontorova model and describes re one-dimensional (1D) composite system made of two subsys tems which are treated on an equal footing. The gap structure of the p honon energy spectrum and the character of lattice vibration are studi ed. We show that the phason mode may be pinned or not depending on the form of the intersubsystem potential. For a weak intersubsystem inter action the structure of the phonon energy spectrum is universal and ma y be revealed by a gnomonic projection of Z(3) onto the plane. For a s hort-range harmonic interaction there ate similarities between this mo del of composite and 1D quasicrystals.