Related papers: Absence of absolutely continuous diffraction spect…
We are interested in a time harmonic acoustic problem in a waveguide with locally perturbed sound hard walls. We consider a setting where an observer generates incident plane waves at $-\infty$ and probes the resulting scattered field at…
We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H \neq 0$, support such modes, here we show…
We show that if a topological insulator is truncated along a curve that separates the plane in two sufficiently large regions, then the edge system admits absolutely continuous spectrum. Our approach combines a recent version of the…
Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube…
Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and…
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic alloys which brought this subject into the limelight. These…
We introduce a procedure for establishing pure discrete spectrum for substitution tiling systems of Pisot family type and illustrate with several examples.
We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless…
The method of coordinate transformation offers a way to realize perfect cloaks, but provides less ability to characterize the performance of a multilayered cloak in practice. Here, we propose an analytical model to predict the performance…
The class of Cyclotomic Aperiodic Substitution Tilings (CAST) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations.…
Concealing objects by making them invisible to an external electromagnetic probe is coined by the term cloaking. Cloaking devices, having numerous potential applications, are still face challenges in realization, especially in the visible…
While practical realizations of optical invisibility have been achieved so far by various ingenious methods, they generally rely on complex materials which prevent the wide implementation of such schemes. Here, we propose an alternative…
The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects…
Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent $\alpha > 0$, that characterizes the power-law scaling behavior of the structure factor $S(\mathbf{k})$ as a function of wavenumber $k\equiv|\mathbf{k}|$…
In this paper, we establish the full-wave electromagnetic scattering theory to study the electromagnetic scattering from infinitely long cylinders with radially anisotropic coatings. We show that the total effective scattering width can be…
Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead…
The goal of this paper is to study the action of the group of translations over self-similar tilings in the euclidian space $\mathbb{R}^d$. It investigates the behaviour near zero for spectral measures for such dynamical systems. Namely the…
We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then…
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…
In this survey of the spectral properties of substitution dynamical systems we consider primitive aperiodic substitutions and associated dynamical systems: ${\mathbb Z}$-actions and ${\mathbb R}$-actions, the latter viewed as tiling flows.…