CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Unitary Scattering Protected by Pseudo-Hermiticity |
L. Jin* |
School of Physics, Nankai University, Tianjin 300071, China |
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Cite this article: |
L. Jin 2022 Chin. Phys. Lett. 39 037302 |
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Abstract Hermitian systems possess unitary scattering. However, the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary. Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity. The energy conservation is violated in the scattering process and recovers after scattering. The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian. These findings provide fundamental insights on the unitary scattering, pseudo-Hermiticity, and energy conservation, and are promising for light propagation, mesoscopic electron transport, and quantum interference in non-Hermitian systems.
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Received: 07 December 2021
Express Letter
Published: 26 January 2022
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[104] | For a rigorous proof, please see Eq. (12) in Ref.[103] and compare the scattering coefficients of the scattering centers $H$ and $H^{\rm T}$. Notice that the symbols $t_{\scriptscriptstyle{\rm L}}$, $t_{\scriptscriptstyle{\rm R}}$, $ r_{\scriptscriptstyle{\rm L}}$ and $r_{\scriptscriptstyle{\rm R}}$ in Ref.[103] are $s_{nm}$, $s_{mn}$, $s_{mm}$ and $s_{nn}$ of the scattering matrix with our current notations for any pair of ports $m$ and $n$. The fact $(A^T)^{-1}=(A^{-1})^T$ is also used in the proof for any square matrix $A$. |
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