Unitary Scattering Protected by Pseudo-Hermiticity

TL;DR

This paper demonstrates that unitary scattering can be protected by pseudo-Hermiticity, even in non-Hermitian systems where energy conservation is temporarily violated during scattering.

Contribution

It proves that certain pseudo-Hermitian structures ensure unitary scattering regardless of the non-Hermiticity degree, revealing fundamental insights into energy conservation and system properties.

Findings

Unitary scattering is protected by pseudo-Hermiticity.

Energy conservation is temporarily violated during scattering.

Subsystems of pseudo-Hermitian centers are Hermitian.

Abstract

The Hermitian systems possess unitary scattering; however, the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary. Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity. The energy conservation is violated in the scattering process and recovers after scattering. The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian. These findings provide fundamental insights on the unitary scattering, pseudo-Hermiticity, and energy conservation; and are promising for the light propagation, mesoscopic electron transport, and quantum interference in the non-Hermitian systems.