Applications of Chebyshev polynomials and Toeplitz theory to topological metamaterials

Q1 Physics and Astronomy
Habib Ammari , Silvio Barandun , Ping Liu
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引用次数: 0

Abstract

We survey the use of Chebyshev polynomials and Toeplitz theory for the study of topological metamaterials. We consider both Hermitian and non-Hermitian systems of subwavelength resonators and provide a mathematical framework to quantitatively explain and characterise some spectacular properties of metamaterials. Our characterisations are based on translation invariance properties of the capacitance matrices associated to the different investigated systems of resonators together with properties of Chebyshev polynomials. The three-term recurrence relation satisfied by the Chebyshev polynomials is shown to be the key to the mathematical analysis of spectra of tridiagonal (perturbed) both Toeplitz (for monomer systems) and 2-Toeplitz (for dimer systems) capacitance matrices.
Chebyshev多项式和Toeplitz理论在拓扑超材料中的应用
本文综述了切比雪夫多项式和Toeplitz理论在拓扑超材料研究中的应用。我们考虑了亚波长谐振子的厄米和非厄米系统,并提供了一个数学框架来定量地解释和表征超材料的一些惊人性质。我们的特征是基于与不同研究系统的谐振器相关的电容矩阵的平移不变性以及切比雪夫多项式的性质。切比舍夫多项式所满足的三项递推关系是三对角线(摄动)Toeplitz(单体体系)和2-Toeplitz(二聚体体系)电容矩阵谱的数学分析的关键。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Reviews in Physics
Reviews in Physics Physics and Astronomy-Physics and Astronomy (all)
CiteScore
21.30
自引率
0.00%
发文量
8
审稿时长
98 days
期刊介绍: Reviews in Physics is a gold open access Journal, publishing review papers on topics in all areas of (applied) physics. The journal provides a platform for researchers who wish to summarize a field of physics research and share this work as widely as possible. The published papers provide an overview of the main developments on a particular topic, with an emphasis on recent developments, and sketch an outlook on future developments. The journal focuses on short review papers (max 15 pages) and these are freely available after publication. All submitted manuscripts are fully peer-reviewed and after acceptance a publication fee is charged to cover all editorial, production, and archiving costs.
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