Reciprocity in parity violating non-Hermitian systems

TL;DR

This paper explores reciprocity in non-Hermitian systems with parity-violating complex potentials, demonstrating that reciprocity can occur under certain conditions even without parity symmetry, including in PT symmetric cases.

Contribution

It extends the understanding of reciprocity to parity-violating complex potentials, providing explicit examples where reciprocity holds beyond symmetric cases.

Findings

Reciprocity holds in PT symmetric complex potentials for all energies.

Reciprocity is observed at discrete energies in other parity-violating potentials.

The study broadens the conditions under which reciprocity can be expected in non-Hermitian systems.

Abstract

Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a PT symmetric (hence parity violating) complex potential which admits penetrating state solutions analytically for all possible values of incidence energy and (ii) reciprocity is shown to hold at certain discrete energies for two other parity violating complex potentials.