Stability of the Non-Hermitian Skin Effect in One Dimension

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-08-05 DOI:10.1137/23m1610537

Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024.
Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.

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一维非赫米提皮肤效应的稳定性

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1697-1717 页，2024 年 8 月。摘要本文通过分析和数值研究表明，非ermitian 亚波长谐振器系统中的趋肤效应对系统中的随机缺陷具有鲁棒性。亚波长谐振器是在低频状态下产生共振的高对比度材料夹杂物。非恒定性是由于引入了一个方向阻尼项（由虚轨势激发），从而导致了集肤效应，表现为系统的特征模型在结构的一个边缘聚集。我们阐明了相关（实）特征频率的拓扑保护，并用数值说明了系统受到随机扰动时两种不同局部化效应之间的竞争：非赫米特趋肤效应和无序诱导的安德森局部化。我们的数值结果表明，随着无序强度的增加，越来越多的特征模在体中局部化。我们的结果基于亚波长物理学的渐近矩阵模型，也可以推广到凝聚态理论中的紧密结合模型。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.