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

TL;DR

This paper investigates phonon transmission, localization, and heat conduction in a 1D Frenkel-Kontorova chain, revealing how external potential influences heat flux and phonon behavior in quasi-periodic systems.

Contribution

It provides a comprehensive analysis of phonon transmission, localization, and heat conduction in the FK model, including all eigenfrequencies and the effect of external potential strength.

Findings

Transmission coefficients vary with eigenfrequency and atom mass.

Phonon localization correlates with transmission and Thouless exponents.

Heat flux scales with system size, influenced by external potential strength.

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.