Fibonacci Chain Polynomials: Identities from Self-Similarity

Wolfdieter Lang

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Fibonacci Chain Polynomials: Identities from Self-Similarity

Wolfdieter Lang

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Abstract

Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbour interaction and two kinds of atoms (mass-ratio $r$) arranged according to the self-similar binary Fibonacci sequence $ABAABABA...$, which is obtained by repeated substitution of $A \to AB$ and $B \to A$. The implications of the self-similarity of this sequence for the associated orthogonal polynomial system which govern these Fibonacci chains with fixed mass-ratio $r$ are studied.

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Wolfdieter Lang. 1994-07-12. Fibonacci Chain Polynomials: Identities from Self-Similarity. https://arxiv.org/abs/cond-mat/9407056

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