Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system

• URL: http://arxiv.org/abs/2011.02097v1
• Date: Wed, 4 Nov 2020 01:56:30 GMT
• Title: Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• Authors: Ken Shobe, Keiichi Kuramoto, Ken-Ichiro Imura, Naomichi Hatano
• Abstract summary: In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity. Here, in contrast, the behavior of the transmission probability is strongly non-Hermitian in the regime of weak non-Hermiticity with divergent peaks.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 find a counter-intuitive 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-Perot-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.

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