Hermitian scattering behavior for the non-Hermitian scattering center

TL;DR

This paper investigates non-Hermitian scattering centers composed of Hermitian clusters with anti-Hermitian couplings, revealing conditions under which they behave as Hermitian and conserve probability, supported by an exactly solvable model.

Contribution

It demonstrates that certain non-Hermitian scattering centers can exhibit Hermitian-like behavior with probability conservation, expanding understanding of non-Hermitian quantum systems.

Findings

The scattering center acts as Hermitian when one cluster is embedded in waveguides.

Probability current conservation occurs despite non-Hermiticity.

Transmission spectra show unique features due to non-Hermitian properties.

Abstract

We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, satisfying $|r| ^{2}+|t| ^{2}=1$, i.e., the Dirac probability current is conserved, when one of two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional PT-symmetric potentials, which is more feasible in experiment. Exactly solvable model is presented to illustrate the theory. Bethe ansatz solution indicates that the transmission spectrum of such a cluster displays peculiar feature arising from the non-Hermiticity of the scattering center.