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The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems.…

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…

In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the…

The vibrational properties of two-dimensional phononic crystals are studied with large-scale molecular dynamics simulations and finite element method calculation. The vibrational band structure derived from the molecular dynamics…

Recently Francoual et al. claimed to have observed the dynamics of long-wavelength phason fluctuations in i-AlPdMn quasicrystals. We will show that the data reported call for a more detailed development of the elasticity theory of Jaric and…

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…

The distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be…

In this chapter, first we will address principal aspects of 1D quasiperiodicity with a particular focus on 1D Fibonacci chains. Further, the rest of the chapter will be dedicated to the electromagnetic counterpart of 1D Fibonacci structures…

In this work, we consider m-bonacci chains, unidimensional quasicrystals obtained by general classes of Rauzy substitutions. Motivated by applications in spectrography and diffraction patterns of some quasicrystals, we pose the problem of…

We theoretically studied the phonon properties of the triangular-, stripe- and honeycomb-type electronic crystals recently found in two-dimensional semiconductor moir\'e patterns. By analyzing the phonon dispersions, we found the…

Phonons diffraction and interference patterns are observed at the atomic scale, using molecular dynamics simulations in systems containing crystalline silicon and nanometric obstacles as voids or amorphous-inclusions. The diffraction…

We demonstrate how supercell implementations of conventional lattice dynamical calculations can be used to determine the extent and nature of disorder-induced broadening in the phonon dispersion spectrum of disordered crystalline materials.…

We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…

We study the Schroedinger equation for an off-diagonal tight-binding hamiltonian, as well as the equations of motion for out-of-plane vibrations, on the separable square Fibonacci quasicrystal. We discuss the nature of the spectra and wave…

We theoretically analyze the spectrum of phonons of a one-dimensional quasiperiodic lattice. We simulate the quasicrystal from the classic system of spring-bound atoms with a force constant modulated by the Aubry-Andr\'e model, so that its…

Understanding the electronic properties of quasicrystals, in particular the dependence of these properties on dimension, is among the interesting open problems in the field of quasicrystals. We investigate an off-diagonal tight-binding…

Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate \textit{ab initio} investigations of lattice anharmonicity encounter difficulties owing to the cumbersome…

Recently de Boissieu et al. proposed an explanation for the broadening of acoustic modes observed in quasicrystals (QC). It is the transcription of a well-known model used for glasses. We raise two fundamental objections against applying it…

From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the…

The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "$2n+1$" theorem to calculate anharmonic…