Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential

TL;DR

This paper reveals conditions under which a non-Hermitian PT-symmetric potential exhibits both reciprocity and unitarity in quantum scattering, including cases of invisibility and pseudo-unitarity, challenging previous assumptions.

Contribution

It demonstrates the simultaneous occurrence of reciprocity and unitarity in PT-symmetric scattering, and introduces the concept of pseudo-unitarity in such systems.

Findings

Potential can be invisible from both sides (R=0, T=1).

Reciprocity and unitarity can coexist in PT-symmetric scattering.

Pseudo-unitarity relation T + sqrt(R_left R_right) = 1 holds in certain regimes.

Abstract

In quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in scattering from a complex PT-symmetric potential. In special cases, we show that this potential can even become invisible (R=0, T=1) from both left and right sides. We also find that this potential in a parametric regime enjoys a pseudo-unitarity of the type $T+\sqrt{R_{left}R_{right}}=1$.