Chin. Phys. Lett.  2021, Vol. 38 Issue (2): 024202    DOI: 10.1088/0256-307X/38/2/024202
Symmetry-Protected Scattering in Non-Hermitian Linear Systems
L. Jin* and Z. Song
School of Physics, Nankai University, Tianjin 300071, China
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L. Jin and Z. Song 2021 Chin. Phys. Lett. 38 024202
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Abstract Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The even-parity symmetries impose strict constraints on the scattering coefficients: the time-reversal ($C$ and $K$) symmetries protect the symmetric transmission or reflection; the pseudo-Hermiticity ($Q$ symmetry) or the inversion ($P$) symmetry protects the symmetric transmission and reflection. For the inversion-combined time-reversal symmetries, the symmetric features on the transmission and reflection interchange. The odd-parity symmetries including the particle-hole symmetry, chiral symmetry, and sublattice symmetry cannot ensure the scattering to be symmetric. These guiding principles are valid for both Hermitian and non-Hermitian linear systems. Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.
Received: 01 December 2020      Published: 04 January 2021
PACS:  03.65.Nk (Scattering theory)  
  03.65.-w (Quantum mechanics)  
  42.82.Et (Waveguides, couplers, and arrays)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11975128 and 11874225).
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