非赫尔密斯皮肤效应的数学基础
Habib Ammari1, Silvio Barandun1, Jinghao Cao1
1Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
Archive for rational mechanics and analysis
|July 11, 2024
概括
我们研究了具有非赫米特潜力的亚波长共振器中的皮肤效应. 大量模式在系统边缘凝结,这种现象与复杂的材料参数效应不同.
科学领域:
- 物理 物理学 物理
- 凝聚物质物理学 凝聚物质物理学
- 波浪现象是一种波浪现象.
背景情况:
- 皮肤效应描述了波浪倾向于在导体表面附近集中.
- 非赫密斯系统表现出独特的特性,这些特性在他们的赫密斯系统中没有.
- 低波长共振器具有独特的电磁和声学特性.
研究的目的:
- 为了研究在有限的单维系统的亚波长共振器的皮肤效应.
- 分析非赫密斯假想测量电位对自态凝聚力的影响.
- 建立一个理论框架,以了解这些系统中的光谱特性.
主要方法:
- 利用Toeplitz矩阵理论来分析系统的光谱属性.
- 为无限周期结构引入一个通用复杂的Brillouin区域.
- 将具有虚拟标量潜力的系统与具有复杂材料参数的系统进行比较.
主要成果:
- 证明了在有限共振器系统的一个边缘的批量固态的凝聚.
- 使用复杂的Brillouin区域计算了相关无限周期结构的光谱带.
- 证明无限系统的光谱带是有限系统的极限.
- 展示了具有虚构测量潜力的非赫密斯系统和具有复杂材料参数的非赫密斯系统之间的基本区别.
结论:
- 这种非赫米斯系统中的皮肤效应导致了散装模式的边缘定位.
- 复杂的Brillouin区域为分析有限和无限非赫米特系统的光谱性质提供了一个强大的工具.
- 通过想象的测量潜力引入的非密性,与复杂的材料参数相比,产生了不同的物理.
关键词:
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