Ground States of a Generalized Frenkel-Kontorova Model**The project partially supported by National Natural Science Foundation of China and Science Foundation of the China Academy of Engineering Physics

Abstract

We studied the modulated structures and commensurate-incommensurate transitions in a generalized Frenkel–Kontorova (FK) model where the chain is composed of three kinds of atoms. For the classical ground states, the phase diagram and the phonon spectrum show the multi-atomic effects. For the quantum ground states, the multi-atomic effects are reflected by the distribution of atoms in external potential, the phase diagram, the correspondences between the ground states and the orbits of the area-preserving maps, as well as the phonon spectrum and coherence length. For the most incommensurate structure, the critical point at which the transition by breaking of analyticity occurs does not vary monotonically with . For the case of and , with the increasing of , the critical point first decreases, then increases. The minimum value of occurs at nearly = 0.035. When , the phonon gap and the Lyapunov exponent , the system is in the sliding state. When , the phonon gap and the Lyapunov exponent show great difference from those of the standard FK model.