Symmetry-Protected Scattering in Non-Hermitian Linear Systems

Symmetry plays fundamental role in physics and the nature of symmetry changes non-Hermitian physics. Here symmetry-protected scattering linear systems is investigated by employing discrete symmetries that classify random matrices. The even-parity impose strict constraints on coefficients: time-reversal (C K) protect symmetric transmission or reflection; pseudo-Hermiticity (Q symmetry) inversion (P) protects reflection. For inversion-combined symmetries, features reflection interchange. odd-parity including particle-hole symmetry, chiral sublattice cannot ensure to be symmetric. These guiding principles are valid for both Hermitian systems. Our findings provide insights into ranging from condensed matter quantum optics.