Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system
In non-Hermitian scattering problems, the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.013223 |
| _version_ | 1827285768777760768 |
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| author | Ken Shobe Keiichi Kuramoto Ken-Ichiro Imura Naomichi Hatano |
| author_facet | Ken Shobe Keiichi Kuramoto Ken-Ichiro Imura Naomichi Hatano |
| author_sort | Ken Shobe |
| collection | DOAJ |
| description | In non-Hermitian scattering problems, the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consider the scattering problem of a PT-symmetric potential, and we find a counterintuitive behavior. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity but observe instability once the non-Hermiticity goes beyond an exceptional point. Here, in contrast, the behavior of the transmission probability is strongly non-Hermitian in the regime of weak non-Hermiticity with divergent peaks, while it is superficially Hermitian in the regime of strong non-Hermiticity, recovering the conventional Fabry-Pérot-type peak structure. We show that the unitarity of the S-matrix is generally broken in both of the regimes, but is recovered in the limit of infinitely strong non-Hermiticity. |
| first_indexed | 2024-04-24T10:20:11Z |
| format | Article |
| id | doaj.art-1c85902bf2dc49a29c524f418c2a2555 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:20:11Z |
| publishDate | 2021-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1c85902bf2dc49a29c524f418c2a25552024-04-12T17:08:05ZengAmerican Physical SocietyPhysical Review Research2643-15642021-03-013101322310.1103/PhysRevResearch.3.013223Non-Hermitian Fabry-Pérot resonances in a PT-symmetric systemKen ShobeKeiichi KuramotoKen-Ichiro ImuraNaomichi HatanoIn non-Hermitian scattering problems, the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consider the scattering problem of a PT-symmetric potential, and we find a counterintuitive behavior. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity but observe instability once the non-Hermiticity goes beyond an exceptional point. Here, in contrast, the behavior of the transmission probability is strongly non-Hermitian in the regime of weak non-Hermiticity with divergent peaks, while it is superficially Hermitian in the regime of strong non-Hermiticity, recovering the conventional Fabry-Pérot-type peak structure. We show that the unitarity of the S-matrix is generally broken in both of the regimes, but is recovered in the limit of infinitely strong non-Hermiticity.http://doi.org/10.1103/PhysRevResearch.3.013223 |
| spellingShingle | Ken Shobe Keiichi Kuramoto Ken-Ichiro Imura Naomichi Hatano Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system Physical Review Research |
| title | Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system |
| title_full | Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system |
| title_fullStr | Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system |
| title_full_unstemmed | Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system |
| title_short | Non-Hermitian Fabry-Pérot resonances in a PT-symmetric system |
| title_sort | non hermitian fabry perot resonances in a pt symmetric system |
| url | http://doi.org/10.1103/PhysRevResearch.3.013223 |
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