Universal estimates for the density of states for aperiodic block subwavelength resonator systems

Fuente: arXiv
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Main Authors: Ammari, Habib, Barandun, Silvio, Davies, Bryn, Hiltunen, Erik Orvehed, Uhlmann, Alexander
Format: Preprint
Published: 2025
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author Ammari, Habib
Barandun, Silvio
Davies, Bryn
Hiltunen, Erik Orvehed
Uhlmann, Alexander
author_facet Ammari, Habib
Barandun, Silvio
Davies, Bryn
Hiltunen, Erik Orvehed
Uhlmann, Alexander
contents 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 $M\to \infty$, the integrated density of states converges to a non-random, continuous function. We show both analytically and numerically that the density of states exhibits a tripartite decomposition: it vanishes identically within bandgaps; it forms smooth, band-like distributions in shared pass bands (a consequence of constructive eigenmode interactions); and, most notably, it exhibits a distinct fractal-like character in hybridisation regions. We demonstrate that this fractal-like behaviour stems from the limited interaction between eigenmodes within these hybridisation regions. Capitalising on this insight, we introduce an efficient meta-atom approach that enables rapid and accurate prediction of the density of states in these hybridisation regions. This approach is shown to extend to systems with quasiperiodic and hyperuniform arrangements of blocks.
format Preprint
id arxiv_https___arxiv_org_abs_2505_16677
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Universal estimates for the density of states for aperiodic block subwavelength resonator systems
Ammari, Habib
Barandun, Silvio
Davies, Bryn
Hiltunen, Erik Orvehed
Uhlmann, Alexander
Mathematical Physics
Disordered Systems and Neural Networks
Materials Science
35J05, 35C20, 35P20, 37A30, 47B36
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 $M\to \infty$, the integrated density of states converges to a non-random, continuous function. We show both analytically and numerically that the density of states exhibits a tripartite decomposition: it vanishes identically within bandgaps; it forms smooth, band-like distributions in shared pass bands (a consequence of constructive eigenmode interactions); and, most notably, it exhibits a distinct fractal-like character in hybridisation regions. We demonstrate that this fractal-like behaviour stems from the limited interaction between eigenmodes within these hybridisation regions. Capitalising on this insight, we introduce an efficient meta-atom approach that enables rapid and accurate prediction of the density of states in these hybridisation regions. This approach is shown to extend to systems with quasiperiodic and hyperuniform arrangements of blocks.
title Universal estimates for the density of states for aperiodic block subwavelength resonator systems
topic Mathematical Physics
Disordered Systems and Neural Networks
Materials Science
35J05, 35C20, 35P20, 37A30, 47B36
url https://arxiv.org/abs/2505.16677