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  • Letter
  • Open Access

Pseudo-Hermiticity protects the energy-difference conservation in the scattering

H. S. Xu and L. Jin*

  • School of Physics, Nankai University, Tianjin 300071, China

  • *jinliang@nankai.edu.cn
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Phys. Rev. Research 5, L042005 – Published 4 October, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042005

Abstract

Symmetry plays a fundamentally important role in physics. In this work, we find a conservation law, S†(Hc†)S(Hc)=I, which is valid for any non-Hermitian scattering center Hc. As a result, the reflections and transmissions of a non-Hermitian system {r,t} and its Hermitian conjugation system {r¯,t¯} satisfy the conservation law r¯*r+t¯*t=1, instead of the energy conservation law that applies to incoming and outgoing waves in a Hermitian system. Consequently, the pseudo-Hermiticity of a non-Hermitian system ensures an energy-difference conservation. Furthermore, we demonstrate that the energy-difference conservation is respectively valid and invalid in two prototypical anti-PT-symmetric systems, where the energy-difference conservation is protected by the pseudo-Hermiticity. Our findings provide profound insight into the conservation law, the pseudo-Hermiticity, and the anti-PT-symmetry in non-Hermitian systems.

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Outline

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Phys. Rev. Research 5, L042005– Published 4 October, 2023
  • Received 26 June 2023
  • Revised 6 September 2023
  • Accepted 14 September 2023
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