Symmetry-Protected Scattering in Non-Hermitian Linear Systems

TL;DR

This paper investigates how discrete symmetries in non-Hermitian linear systems influence scattering properties, revealing which symmetries protect symmetric transmission and reflection, applicable across various physical systems.

Contribution

It provides a comprehensive classification of symmetry-protected scattering behaviors in non-Hermitian systems based on discrete symmetries, extending understanding beyond Hermitian cases.

Findings

Even-parity symmetries impose strict constraints on scattering coefficients.

Time-reversal and pseudo-Hermiticity symmetries protect symmetric transmission or reflection.

Inversion combined with time-reversal symmetries interchange symmetric features.

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.