The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case

TL;DR

This paper computes the spectral measure for orthogonal polynomials associated with periodic Fibonacci chains, using two methods, and relates it to Green's functions, advancing understanding of spectral properties in these systems.

Contribution

It introduces two methods for computing spectral measures of orthogonal polynomials related to periodic Fibonacci chains and links these measures to Green's functions.

Findings

Spectral measures for Fibonacci chain-related orthogonal polynomials are explicitly computed.

The relation between spectral measures and Green's functions is established.

Results enhance understanding of spectral properties in periodic Fibonacci systems.

Abstract

The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.