相关论文: Sound modes broadening for Fibonacci one dimension…
Recently, Engel et al. discussed phonon broadening as observed in 3D quasicrystals on the basis of calculations on the Fibonacci chain. We show that the paper contains several statements and assumptions that are contradicted by factual…
The Fibonacci chain, i.e., a tight-binding model where couplings and/or on-site potentials can take only two different values distributed according to the Fibonacci word, is a classical example of a one-dimensional quasicrystal. With its…
We propose a simple phenomenological model to analyze vibrational characteristics of quasicrystals (QCs). The interpretation of the obtained recently data is based on the existence of almost dispersionless optical modes most probably…
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…
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…
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…
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…
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.…
Fibonacci time quasicrystals can be approximated by temporal supercells to reveal a fractal collection of $k$ gaps, in which wave energy is amplified exponentially. These estimates are validated by the observation of "super" $k$ gaps that…
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…
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…
Open phononic systems including resonators radiating inside an unbounded medium support localized phonons characterized by a complex frequency. In this context, the concept of elastic quasinormal mode (QNM) arises naturally, as in the cases…
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…
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…
A recently proposed modified perturbation expansion for QCD is employed to evaluate the quark self-energies. Results of the order of 1/3 of the nucleon mass are obtained for the effective masses of the up and down quarks in a first…
A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the…
We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H\"older…
Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffraction and dynamical spectra. In one dimension, we consider…
We study the emergence of quasiperiodic Bloch wave functions in quasicrystals, employing the one-dimensional Fibonacci model as a test case. We find that despite the fact that Bloch functions are not eigenfunctions themselves,…
In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as ${\cal R}\propto a^3$. This is so far the only known class of self-consistent…