Express Letter
Unitary Scattering Protected by Pseudo-Hermiticity
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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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References
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The fact A^T^{-1}=A^{-1}^TA^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 rL=−tRr∗R/t∗L. 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}}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}}.[106] [1] -
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