Sound modes broadening for Fibonacci one dimensional quasicrystals

TL;DR

This paper studies vibrational mode broadening in one-dimensional Fibonacci quasicrystals, revealing universal frequency dependence and larger broadening compared to simpler crystal structures, with potential extensions to three dimensions.

Contribution

It introduces a self-consistent approach to calculate vibrational broadening in Fibonacci quasicrystals and demonstrates universal behavior across 1D and 3D systems.

Findings

Broadening depends universally on frequency in intermediate coupling regimes.

Systems with non-simple elementary cells exhibit larger broadening.

Method can be extended to three-dimensional quasicrystals.

Abstract

We investigate vibrational excitation broadening in one dimensional Fibonacci model of quasicrystals (QCs). The chain is constructed from particles with two masses following the Fibonacci inflation rule. The eigenmode spectrum depends crucially on the mass ratio. We calculate the eigenstates and eigenfunctions. All calculations performed self-consistently within the regular expansion over the three wave coupling constant. The approach can be extended to three dimensional systems. We find that in the intermediate range of mode coupling constants, three-wave broadening for the both types of systems (1D Fibonacci and 3D QCs) depends universally on frequency. Our general qualitative conclusion is that for a system with a non-simple elementary cell phonon spectrum broadening is always larger than for a system with a primitive cell (provided all other characteristics are the same).