Related papers: Construction of a dispersion relation from an arbi…
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…
An angular effective mass formalism previously introduced is used to study the density of states in warped and non-warped energy bands. Band warping may or may not increase the density-of-states effective mass. Band "corrugation," referring…
We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…
We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…
We consider the spectral properties of aperiodic block subwavelength resonator systems in one dimension, with a primary focus on the density of states. We prove that for random block configurations, as the number of blocks $M\to \infty$,…
Effects of the band structure on the symmetry of superconducting (SC) states are studied. For a square lattice system with a nearest-neighbor attractive interaction, SC states with various symmetries are found by changing the band…
Flat bands result in a divergent density of states and high sensitivity to interactions in physical systems. While such bands are well known in systems under magnetic fields, their realization and behavior in zero-field settings remain…
Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…
Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we determine densities of states in materials with low dimensional substructures and relativistic dispersion relations. We find that these…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
The motion of an electron in an image field and a blocking electric field is considered in semiclassical approximation. An exact analytical expression is found for the density of the energy spectrum of states. The dependence of spectral…
We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both…
The band structure of photons in cholesteric liquid crystals (CLCs) is investigated in the shortwave approximation. The bound states or narrow resonances of photons in the CLC are formed by the extraordinary waves. The explicit expressions…
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
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…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…