Structural transitions and phonon localization in frenkel kontorova models with quasi-periodic potentials

Abstract

We have studied the ground state and phonons of a generalized Frenkel Kontorova model with a quasiperiodic substrate potential. We have recently shown that, depending on the three mutually incommensurate, relevant lengths, a sliding mode below a critical coupling can either occur or be absent although a structural transition takes place in both cases. Besides, we observe a transition to localized phonon states. Here we investigate the structural and localization transitions in terms of a nonlinear discrete map.