Non-Hermitian Topology and Exceptional-Point Geometries
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909210528186368 |
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| author | Ding, Kun Fang, Chen Ma, Guancong |
| author_facet | Ding, Kun Fang, Chen Ma, Guancong |
| contents | Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this paper, we comprehensively review non-Hermitian topology by establishing its relationship with the behaviors of complex eigenvalues and biorthogonal eigenvectors. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11601 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Topology and Exceptional-Point Geometries Ding, Kun Fang, Chen Ma, Guancong Quantum Physics Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this paper, we comprehensively review non-Hermitian topology by establishing its relationship with the behaviors of complex eigenvalues and biorthogonal eigenvectors. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications |
| title | Non-Hermitian Topology and Exceptional-Point Geometries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2204.11601 |