Wave transmission, phonon localization and heat conduction of 1D Frenkel-Kontorova chain

Abstract

We study the transmission coefficient of a plane wave through a 1D finite quasi-periodic 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 {\it 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 Rubin-Greer-like model for FK chain at low temperature is calculated. It is found that the stationary heat flux $J(N)\sim N^{\alpha }$, and $\alpha$ depends on the strength of the external potential.

15 pages in Revtex, 8 EPS figures

References in corpus (1)

• Energy transport and correlation between two attractors connected by Fermi-Pasta-Ulam chain

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