Pure skin effect obeying power partition in directed graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909178325368832 |
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| author | Liu, Wenwen You, Oubo Min, Bumki Zhang, Shuang |
| author_facet | Liu, Wenwen You, Oubo Min, Bumki Zhang, Shuang |
| contents | Non-Hermitian physics has received great attention recently. In particular, band structures in non-Hermitian systems can be engineered to exhibit various topological effects. Among them, one of the most intriguing phenomena is the non-Hermitian skin effect (NHSE). Here, we investigate NHSE in systems featuring directed chains or directed graphs, where the arrows denote the directions of the non-reciprocal hopping between neighbouring nodes. We show that the systems exhibit pure skin modes with non-oscillatory wavefunctions, in contrast to previously studied NHSE. Interestingly, the sum of the decay constants along different directions for each skin mode obeys a power partition rule, i.e. their sum is a fixed value and the value of each constant only depends on the ratio between the non-reciprocal hopping parameters and is independent of detailed graph configurations. Such Pure Skin Effect (PSE) can be explained by using a generalized method for solving the Generalized Brillouin-zone with multiple bulk states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_14727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pure skin effect obeying power partition in directed graphs Liu, Wenwen You, Oubo Min, Bumki Zhang, Shuang Quantum Physics Applied Physics Optics Non-Hermitian physics has received great attention recently. In particular, band structures in non-Hermitian systems can be engineered to exhibit various topological effects. Among them, one of the most intriguing phenomena is the non-Hermitian skin effect (NHSE). Here, we investigate NHSE in systems featuring directed chains or directed graphs, where the arrows denote the directions of the non-reciprocal hopping between neighbouring nodes. We show that the systems exhibit pure skin modes with non-oscillatory wavefunctions, in contrast to previously studied NHSE. Interestingly, the sum of the decay constants along different directions for each skin mode obeys a power partition rule, i.e. their sum is a fixed value and the value of each constant only depends on the ratio between the non-reciprocal hopping parameters and is independent of detailed graph configurations. Such Pure Skin Effect (PSE) can be explained by using a generalized method for solving the Generalized Brillouin-zone with multiple bulk states. |
| title | Pure skin effect obeying power partition in directed graphs |
| topic | Quantum Physics Applied Physics Optics |
| url | https://arxiv.org/abs/2404.14727 |