Mathematical Theory For Supercell Approximations Of Fibonacci Quasicrystals

Davies B.

;Morini L.

2023-01-01

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Abstract

We present mathematical theory showing that supercell approximations accurately predict the main spectral gaps of Fibonacci quasicrystals. This theory is based on characterising the growth of the underlying recursion relation and corroborates the existence of previously observed 'super band gaps'. We demonstrate our general theory through application to a one-dimensional metamaterial, composed of a system of structured rods.