Topological enhancement of non-normality in non-Hermitian skin effects
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916264147943424 |
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| author | Nakai, Yusuke O. Okuma, Nobuyuki Nakamura, Daichi Shimomura, Kenji Sato, Masatoshi |
| author_facet | Nakai, Yusuke O. Okuma, Nobuyuki Nakamura, Daichi Shimomura, Kenji Sato, Masatoshi |
| contents | The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06689 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological enhancement of non-normality in non-Hermitian skin effects Nakai, Yusuke O. Okuma, Nobuyuki Nakamura, Daichi Shimomura, Kenji Sato, Masatoshi Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics Optics Quantum Physics The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem. |
| title | Topological enhancement of non-normality in non-Hermitian skin effects |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics Optics Quantum Physics |
| url | https://arxiv.org/abs/2304.06689 |