Thermal conductivity of one-dimensional Fibonacci quasicrystals

Abstract

We consider a general Fibonacci quasicrystal (FQC) in which both the masses and the elastic constants are aperiodically arranged. Making use of a suitable decimation scheme, inspired by real-space renormalization-group concepts, we obtain closed analytical expressions for the global transfer matrix and transmission coefficient for several resonant critical normal modes. The fractal structure of the frequency spectrum significantly influences both the cumulative contribution of the different normal modes to the thermal transport and the dependence of the thermal conductivity with the temperature over a wide temperature range. The role of resonant effects in the heat transport through the FQC is numerically and analytically discussed.