Related papers: Hierarchical Band Gaps in Complex Periodic Systems
Cellular materials not only show interesting static properties but can also be used to manipulate dynamic mechanical waves. In this contribution, the existence of phononic band gaps in periodic cellular structures is experimentally shown…
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is…
We will discuss a somewhat striking spectral property of finitely valued stationary processes on Z that says that if the spectral measure of the process has a gap then the process is periodic. We will give some extensions of this result and…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
It is well-known that band gaps, in the frequency domain, can be achieved by using periodic metamaterials. However it has been challenging to design materials with broad band gaps or that have multiple overlapping band gaps. For periodic…
This paper demonstrates that complex PT-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
Periodic structures are a type of metamaterial in which the physical properties depend not only on the details of the unit cell but also on how unit cells are arranged and interact with each other. In conventional engineering structures,…
The spectrum of periodic differential operators typically exhibits a band-gap structure. In this paper, we will consider perturbations to periodic differential operators and investigate the spectrum the perturbation induces in the gaps.…
A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.
While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework…
It is demonstrated theoretically that the strong interaction between electrons in periodical structures and a high-frequency electromagnetic field suppresses the Bragg reflection of the electrons. As a result, the band gaps in electron…
We present mathematical theory for understanding the transmission spectra of heterogeneous materials formed by generalised Fibonacci tilings. Our results, firstly, characterise super band gaps, which are spectral gaps that exist for any…
Characteristic modes of arbitrary two-dimensional periodic systems are analyzed using scattering parameter data. This approach bypasses the need for periodic integral equations and allows for characteristic modes to be computed from generic…
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period…