Ammari Habib, Barandun Silvio, Cao Jinghao, Davies Bryn, Hiltunen Erik Orvehed
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ UK.
Arch Ration Mech Anal. 2024;248(3):33. doi: 10.1007/s00205-024-01976-y. Epub 2024 Apr 6.
We study the skin effect in a one-dimensional system of finitely many subwavelength resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we prove the condensation of bulk eigenmodes at one of the edges of the system. By introducing a generalised (complex) Brillouin zone, we can compute spectral bands of the associated infinitely periodic structure and prove that this is the limit of the spectra of the finite structures with arbitrarily large size. Finally, we contrast the non-Hermitian systems with imaginary gauge potentials considered here with systems where the non-Hermiticity arises due to complex material parameters, showing that the two systems are fundamentally distinct.
我们研究了具有非厄米虚规范势的有限多个亚波长谐振器的一维系统中的趋肤效应。利用托普利兹矩阵理论，我们证明了体态本征模在系统的一条边缘处发生凝聚。通过引入广义（复）布里渊区，我们可以计算相关无限周期结构的能带，并证明这是任意大尺寸有限结构光谱的极限。最后，我们将这里考虑的具有虚规范势的非厄米系统与由于复材料参数而产生非厄米性的系统进行对比，表明这两个系统在本质上是不同的。
