Wave transmission, phonon localization, and heat conduction of a one-dimensional Frenkel-Kontorova chain

We study the transmission coefficient of a plane wave through a one-dimensional finite quasiperiodic system-the Frenkel-Kontorova (FK) model-embedding in an infinite uniform harmonic chain. By varying the mass of atoms in the infinite uniform chain, we obtain the transmission coefficients for all eigenfrequencies. The phonon localization of the incommensurated FK chain is also studied in terms of the transmission coefficients and the Thouless exponents. Moreover, the heat conduction of the Rubin-Greer-like model for the FK chain at low temperature is calculated. It is found that the stationary heat flux J(N)∼N^α, and α depends on the strength of the external potential.