| 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: |
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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 $A$. |
| [105] | From the off-diagonal term of $SS^{† }$, we obtain $r_{\scriptscriptstyle{\rm L}}=-t_{\scriptscriptstyle{\rm R}}r_{\scriptscriptstyle{\rm R}}^{\ast }/t_{\scriptscriptstyle{\rm L}}^{\ast }$. From the diagonal terms of $SS^{† }$, we obtain $1=r_{\scriptscriptstyle{\rm L}}r_{\scriptscriptstyle{\rm L}}^{\ast }+t_{\scriptscriptstyle{\rm R}}t_{\scriptscriptstyle{\rm R}}^{\ast }=\left( r_{\scriptscriptstyle{\rm R}}^{\ast }r_{\scriptscriptstyle{\rm R}}/t_{\scriptscriptstyle{\rm L}}^{\ast }t_{\scriptscriptstyle{\rm L}}+1\right) t_{\scriptscriptstyle{\rm R}}t_{\scriptscriptstyle{\rm R}}^{\ast }=t_{\scriptscriptstyle{\rm R}}t_{\scriptscriptstyle{\rm R}}^{\ast }/t_{\scriptscriptstyle{\rm L}}^{\ast }t_{\scriptscriptstyle{\rm L}}$. |
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