Maciá Barber, Enrique Alfonso2023-06-202023-06-202006-051098-012110.1103/PhysRevB.73.184303https://hdl.handle.net/20.500.14352/52107©2006 The American Physical Society. This work has been supported by the Universidad Complutense de Madrid through Project No. PR27/05-14014-BSCH. I warmly thank Víctor R. Velasco, Gerardo G. Naumis, and Rogelio Rodríguez-Oliveros for very useful comments and Victoria Hernández for a critical reading of the manuscript.We study the phonon dynamics of Fibonacci heterostructures where two kinds of order (namely, periodic and quasiperiodic) coexist in the same sample at different length scales. We derive analytical expressions describing the dispersion relation of finite Fibonacci superlattices in terms of nested Chebyshev polynomials of the first and second kinds. In this way, we introduce a unified description of the phonon dynamics of Fibonacci heterostructures, able to exploit their characteristic hierarchical structure in a natural way.engjournal articlehttp://dx.doi.org/10.1103/PhysRevB.73.184303https://journals.aps.orgopen access538.9Singular continuous-spectrumQuasi-periodic structuresCritical wave-functionsSchrodinger-operatorsThermal-conductivityPhysical natureCantor-setModelCrystalsSystemsFísica de materialesFísica del estado sólido2211 Física del Estado Sólido