Related papers: Exponentially localised interface eigenmodes in fi…
The transmission coefficient for a one dimensional system is given in terms of Chebyshev polynomials using the tight-binding model. This result is applied to a system composed of two impurities located between $N$ sites of a host lattice.…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
Bragg scattering in periodic media generates band gaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these band gaps. This is caused by boundary…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces.…
Among the remarkable scattering properties of correlated disordered materials, the origin of pseudo-gaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves…
Reentrant localization transitions, that is, the transitions of a portion of the eigenspectrum from localized to critical and then again to localized as the disorder strength is increased, have been recently unveiled in various…
Using a Multiple Scattering Theory algorithm, we investigate numerically the transmission of ultrasonic waves through a disordered locally resonant metamaterial containing only monopolar resonators. By comparing the cases of a perfectly…
Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of…
A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes…
Optical embedded eigenstates are localized modes of an open structure that are compatible to radiation yet they have infinite lifetime and diverging quality factors. Their realization in nanostructures finite in all dimensions is inherently…
Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a…
In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes…
We propose a decentralized subspace algorithm for identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be…
Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and…
Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the…
We consider the problem of parallelizing electronic structure computations in plane-wave Density Functional Theory. Because of the limited scalability of Fourier transforms, parallelism has to be found at the eigensolver level. We show how…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
We theoretically demonstrate the concept of metadamping in dissipative metamaterials. We consider an infinite mass-spring chain with repeated local resonators and a statically equivalent periodic chain whose wave propagation characteristics…
We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of $\beta$-damped stationary solutions cannot be completely…